EXTRA PRACTICE EXERCISES
688 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 1
Addition and Subtraction of Real Numbers
Use after Sections 1.5 and 1.6 Name ____________________________
Examples: Add.
a)
5+9=14
−5+9=4 b)
()
()
594
5914
+− =−
−+− =− c)
()
5 2 15 16 1
8 3 24 24 24
6. 7 8.1 1.4
−+ =− + =
+− =−
Add.
1.
()
45−+− = ______________________ 2. 76−+ = __________________________
3.
()
83+− = ________________________ 4. 88−+ =
__________________________
5.
()
11 17−+− = _____________________ 6. 15 3−+= _________________________
7. 615−+ = ________________________ 8.
()
57+− = _________________________
9.
()
18 3+− = _______________________ 10.
()
919−+− = _______________________
11. 92−+ = _________________________ 12.
()
67+− = _________________________
13.
()
31−+− = _______________________ 14.
()
44−+− = ________________________
15.
()
18 15+− = ______________________ 16. 15 4−+=
_________________________
17. 719−+ = ________________________ 18.
()
16 9+− = ________________________
19.
()
24 11+− = ______________________ 20. 56−+ = __________________________
21.
()
39−+− = ______________________ 22.
()
12 7+− = ________________________
23. 714−+ = ________________________ 24.
()
25−+− = ________________________
25. 21 21−+ = _______________________ 26. 82−+ = __________________________
27.
()
911+− = _______________________ 28.
()
511−+− = _______________________
29. 32
45
§·
−+− =
¨¸
©¹
_____________________ 30. 73
84
§·
+− =
¨¸
©¹
_______________________
31. 52
12 3
−+=
_______________________ 32. 11
53
§·
−+− =
¨¸
©¹
______________________
33. 71
94
§·
+− =
¨¸
©¹
______________________ 34. 15
27
−+= _________________________
35. 9.5 4.3−+ = ______________________ 36. 8.7 15.2−+ = _______________________
37.
()
3.1 6.8−+− = ____________________ 38.
()
15.6 19.2+− = ____________________
39. 7.5 9.1−+ = ______________________ 40.
()
6.5 9.9−+− = _____________________
Extra Practice Exercises 689
EXTRA PRACTICE 1 (continued)
Addition And Subtraction Of Real Numbers
Use after Sections 1.5 and 1.6
Examples: Subtract.
6−9=6+(−9) =−3
−6−9=−6+(−9) =−15
6−(−9) =6+9=15
−6−(−9) =−6+9=3
()
2 4 10 12 22
3 5 15 15 15
6.9 5.2 6.9 5.2 12.1
§·
− − =− + − =−
¨¸
©¹
−− = + =
Subtract.
41. 610−− = ________________________ 42.
()
77−−− = ________________________
43.
()
15 3−− = _______________________ 44. 611−= ___________________________
45. 912−− = ________________________ 46.
()
815−−− = _______________________
47. 38−=
__________________________ 48. 73−− =
__________________________
49.
()
56−−− = ______________________ 50.
()
113−− = ________________________
51.
()
74−−− = ______________________ 52. 82−− =
__________________________
53.
()
92−− = ________________________ 54.
()
19 6−−−= _______________________
55. 716−= _________________________ 56. 15 3−= ___________________________
57. 15 4−−= ________________________ 58.
()
58−− = _________________________
59.
()
97−−− = ______________________ 60. 611−= ___________________________
61.
()
56−− = ________________________ 62.
()
15 7−−−= _______________________
63. 315−= __________________________ 64.
()
68−− = _________________________
65. 26−− = _________________________ 66. 17 21−= __________________________
67.
()
19 4−− = _______________________ 68.
()
612−−− = _______________________
69. 51
82
−=
__________________________ 70. 32
43
−−=
_________________________
71. 93
10 4
§·
−−− =
¨¸
©¹
____________________ 72. 11
56
−− =
_________________________
73. 72
12 5
§·
−− =
¨¸
©¹
______________________ 74. 55
96
§·
−−− =
¨¸
©¹
______________________
75.
()
7.8 13.2−− = ____________________ 76. 4.1 16.3−− =
_______________________
77. 8.7 12.4−=
_______________________ 78.
()
8.2 5.5−−− = _____________________
79. 5.3 1.8−− =
_______________________ 80.
()
6.9 3.4−− = ______________________
690 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 2
Multiplication and Division of Real Numbers
Use after Section 1.7 Name ____________________________
Examples: Multiply.
a)
5⋅6=30
−5⋅6=−30 b)5(6) 30
5(6) 30
⋅− =−
−⋅− = c)
()()
52 10 5
83 24 12
35 79 27.65
§·
− ⋅ =− =−
¨¸
©¹
−⋅ ⋅−⋅ =
Multiply.
1. 73−⋅ = __________________________ 2.
()
98⋅− = __________________________
3. 11 4−⋅= _________________________ 4.
()
74−⋅− = ________________________
5.
()
16 4⋅− = ________________________ 6.
()
13 11−⋅− = _______________________
7. 21 5−⋅= _________________________ 8.
()
10 2⋅− = _________________________
9. 65−⋅ = __________________________ 10.
()
20 9⋅− = ________________________
11.
()
813−⋅− = ______________________ 12.
()
311−⋅− = ________________________
13. 19 5−⋅= _________________________ 14. 15 12−⋅ = _________________________
15.
()
16 9⋅− = ________________________ 16.
()
715−⋅− = _______________________
17.
()
412⋅− = _______________________ 18. 912−⋅ = __________________________
19.
()
327−⋅− = ______________________ 20.
()
15 8⋅− = _________________________
21.
()
19 3−⋅−= ______________________ 22.
()
15 9−⋅−= _______________________
23.
()
17 5⋅− = ________________________ 24. 24 7−⋅= __________________________
25. 26
37
§·
⋅− =
¨¸
©¹
_______________________ 26. 510
89
−⋅ =
_________________________
27. 415
516
§·
−⋅− =
¨¸
©¹
_____________________ 28. 75
10 14
§·
⋅− =
¨¸
©¹
_______________________
29. 16 9
38
−⋅= ________________________ 30. 316
427
§·
−⋅− =
¨¸
©¹
______________________
31.
()( )
0.8 0.9⋅− = ____________________ 32. 4.5 6.8−× =
________________________
33.
()
973−⋅−⋅ = _____________________ 34.
()( )
1. 5 5. 8⋅− = ______________________
35. 3.7 6.6−× =
_______________________ 36.
()()
8.3 4.6−⋅−= ____________________
Extra Practice Exercises 691
EXTRA PRACTICE 2 (continued)
Multiplication and Division of Real Numbers
Use after Section 1.7
Examples: Divide.
a)15 3 5
15 3 5
÷=
−÷=−
b)
()
()
15 3 5
15 3 5
÷− =−
−÷−=
c)7372147
8 2 8 3 24 12
8.4 2.1 4
§· §·
−÷−=−⋅−==
¨¸ ¨¸
©¹ ©¹
−÷ =−
Divide.
37. 75 5÷=
_________________________ 38. 78 3−÷=
_________________________
39.
()
413 7÷− = ______________________ 40.
()
300 12−÷−= _____________________
41. 126 21−÷=
______________________ 42.
()
595 5−÷−= ______________________
43.
()
270 15÷− = _____________________ 44. 156 26−÷=
_______________________
45.
()
275 11÷− = _____________________ 46.
()
270 30−÷−= _____________________
47. 95 19−÷=
_______________________ 48.
()
168 14−÷−= _____________________
49. 576 32−÷= ______________________ 50. 39 13÷= __________________________
51.
()
198 18−÷−= ____________________ 52.
()
320 16÷− = ______________________
53. 384 24−÷= ______________________ 54. 152 19−÷= ________________________
55.
()
336 21−÷−= ____________________ 56. 195 13−÷= ________________________
57.
()
288 9−÷−= _____________________ 58.
()
160 32−÷−= _____________________
59. 135 15−÷= ______________________ 60.
()
153 51−÷−= _____________________
61. 35
42
§·
÷− =
¨¸
©¹
______________________ 62. 59
816
−÷ = _________________________
63. 82
927
§·
−÷− =
¨¸
©¹
____________________ 64. 510
721
§·
÷− =
¨¸
©¹
______________________
65. 55
44
−÷= ________________________ 66. 28
39
§·
−÷− =
¨¸
©¹
______________________
67. 15.5 3.1÷= _______________________ 68. 9.9 3.3−÷ = ________________________
69.
()
21.5 4.3−÷−= ___________________ 70.
()
14.4 1.2÷− = _____________________
71.
()
5.234 0.5−÷= ___________________ 72. 34.84 6.7−÷= _____________________
692 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 3
Exponential Notation and Order of Operations
Use after Section 1.8 Name _________________________
_
Examples.
a) Write exponential notation for 8·8·8·8.
The exponential notation is 84.
b) Simplify using order of operations:
c) Evaluate
()
253 ,x+÷for x=8.
Write in exponential notation.
1. 6⋅6⋅6 ___________ 2. 14⋅14 ⋅14 ⋅14 ⋅14 ____________
3. t⋅t⋅t⋅t ___________ 4. 2
x
⋅2
x
⋅2
x
⋅2
x
⋅2
x
⋅2
x
⋅2
x
⋅2
x
__________________
Simplify.
5. 2
6 ___________ 6.
()
3
4− ____________
7. 5
3 ___________ 8.
()
7
1− ____________
9. 2
8 ___________ 10.
()
4
2− ____________
11.
()
1
4− ___________ 12. 3
5 ____________
13.
()
2
8
x
___________ 14.
()
3
2
x
− ____________
15. 823+⋅ ___________ 16. 64 7⋅− ____________
17. 684+÷ ___________ 18. 72 6 3⋅−÷ ____________
19. 3 7 1 4+÷+ ___________ 20. 6 2 4 1⋅÷− ____________
21. 2
72+ ___________ 22.
()
2
72+ ____________
23. 642+÷ ___________ 24.
()
64 2+÷ ____________
25.
()
32 2 6÷− + ___________ 26.
()( )
82 62⋅− −− ÷ ____________
()
()
2
57385
25 7 5 5
25 35 5
60 5
65
−−+
−−+
++
+
()
()
()
28 5 3
16 5 3
21 3
7
=+÷
=+÷
=÷
=
Extra Practice Exercises 693
EXTRA PRACTICE 3 (continued)
Exponential Notation and Order of Operations
Use after Section 1.8
Simplify.
27. 32⋅23+ 4 ___________ 28. 42+3⋅9 ____________
29.
()
()
22
294 102−+ ÷ ÷ ___________ 30.
()
()
3
36 4 7 4
ªº
÷⋅−
¬¼
____________
31.
18 ÷2
22−1 ___________ 32.
()
2
8431635−⋅+ ÷ + ____________
33.
()
432 2−⋅ ÷− ___________ 34.
()
2
6674 35−⋅+ − ⋅ ____________
35.
()
2
652 10 8
ªº
+−÷
¬¼
___________
Evaluate.
36. 8 3 , for 1xx+=− ___________ 37. 4
24 , for 2tt−=
____________
38.
()
12 2 , for 3ss÷=− ___________ 39. 16 5 4, for 5mm−+ = ____________
40.
()
22 4 , for 2rr r−+ =− ___________ 41.
()
3 7 4, for 3xx+÷ = ____________
42.
()
()
210 2 5 , for 4aa a−÷÷− = 43.
2
( 3) 11 , for 1ccc−− − =− ____________
___________
Rename each expression without using parentheses.
44.
()
73x−− + ___________ 45.
()
58
x
−+ ____________
46.
()
49abc−− − ___________ 47.
()
2
5102cc−+− ____________
Remove parentheses and simplify.
48.
()
241yy−+ ___________ 49.
()
382qq−− ____________
50.
()
6103ss−− ___________ 51.
()
1dd−− ____________
52.
()
342
x
xx+− − ___________ 53. 2 3 4(2 )en en+− − ____________
54.
()
625 2
x
yxy−− + ___________ 55.
()
22
423 2xxx+− + ____________
56.
()
2222
524223aabb ab−− + − − 57.
()()
4537
x
x−− − ____________
___________
58.
() ()
22
342721xxx x−+− + _________ 59.
()()
52 3 4 1 2xx+−ª−+º
¬¼
____________
60.
()
()
22
2763
x
xx
ªº
+− +−
__________
694 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 4
Problem Solving
Use after Section 2.5 Name ____________________________
Example: Three plus six times a number is 7 more than four times the number. What is the
number?
Three plus six times a number is 7 more than four times the number.
36 7 4xx
↓↓ ↓
↓↓↓↓ ↓↓ ↓↓
+=+⋅
⋅
Solve:
36 74
32 7
24
2
x
x
x
x
x
+=+
+=
=
=
Solve.
1. When 6 is added to three times a number, the result is 30. Find the number.
________________
2. When you double a number and then add 20, you get 4
3of the original number. Find the
number. ________________
3. The perimeter of a rectangle is 52 cm. The length is 8 cm greater than the width. Find the
width and length. ________________
4. The perimeter of a rectangle is 78 m. The width is 7 m less than the length. Find the length
and width. ________________
5. The sum of three consecutive even integers is 150. Find the integers. ________________
Extra Practice Exercises 695
EXTRA PRACTICE 4 (continued)
Problem Solving
Use after Section 2.5
6. The sum of three consecutive odd integers is 261. Find the integers. ________________
7. A 20-ft board is cut into three pieces. The second piece is three times as long as the first.
The third piece is twice as long as the second. Find the lengths of the pieces. ________________
8. Ⱥ 450-m fence is divided into three sections. The second section is twice as long as the first.
The third section is three times as long as the second. Find the lengths of the sections.
________________
9. The second angle of a triangle is three times as large as the first. The third angle is 20° larger
than the sum of the first two. Find the measures of the angles. ________________
10. The second angle of a triangle is twice as large as the first. The third angle is 50° less than
the second. Find the measures of the angles. ________________
11. The cost of renting a car is $18 per day plus 16¢ per mile. Find the cost of renting a car for a
three-day trip of 1000 miles. ________________
12. Thirteen less than twice a number is seventeen more than half the number. What is the
number? ________________
696 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 5
Solving Inequalities
Use after Section 2.6 Name ____________________________
Examples: Solve.
a)
596
515
3
x
x
x
−>
>
>
b)
4379
3 6
2
xx
x
x
+≤ +
−≤
≥−
The solution set is
{
}
|3.xx> The solution set is
{
}
|2.xx≥−
Solve.
1. 3 9y+> _________________________ 2. 73x−≥−
_________________________
3. 535x< __________________________ 4. 328a+≥ _________________________
5. 8374xx+< + ____________________ 6. 9 63y−> __________________________
7. 5 9 2x−≥ ________________________ 8. 3 4 2x+≤− ________________________
9. 10 7 2 17yy−>− + _________________ 10. 3 1 8 24tt−≤ + _____________________
11. 37
4x< __________________________ 12. 8 7 3 2yy−>− _____________________
13. 6 5 4 7yy+≥ + ____________________ 14. 2 1 5 7mm−≥ − ____________________
Extra Practice Exercises 697
EXTRA PRACTICE 5 (continued)
Solving Inequalities
Use after Section 2.6
15. 56 9
x
x+>−
_____________________ 16. 10 7 7 5
x
x+≤ − ____________________
17. 3116x+< _______________________ 18. 5 4 21x−> ________________________
19. 8117 2yy−≥ + ___________________ 20. 3 4 7 16mm−< − ___________________
21. 1
34
x−≤ _________________________ 22. 36
2y>− __________________________
23. 2 3 4xx+≥ − ____________________ 24. 7 2 15xx<+ _______________________
25. 11
23
x−> ________________________ 26. 25
36
y+≤ ________________________________________
27. 15 3 4 13xx−>− __________________ 28. 25 83
x
x−< +− ________________________________
29. 17 5 4y<− _______________________ 30. 31 7 6y>− ______________________________________
698 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 6
Graphing Linear Equations
Use after Section 3.2 Name ____________________________
ȿɯɚmɪlɟ: Graph. 2yx=−
x
y (x,y)
y=x−2
−2 −4
()
2, 4−−
−1 −3
()
1, 3−−
0 −2
()
0, 2−
1 −1
()
1, 1−
2 0
()
2, 0
y
y = x – 2
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
1. y=3x+1
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
2. 2 3yx=− 3. 4yx=+ 4. 3 2yx=− +
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
5. 32
2
yx=+
6. yx=− 7. 5yx=+
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 699
EXTRA PRACTICE 6 (continued)
Graphing Linear Equations
Use after Section 3.2
8. y=−3x−1 9. 5yx=− 10. y=2
3x−1
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
11. 3 2yx=− 12. 4yx=− − 13. 3yx=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
14. y=2x+3 15.
12
3
yx=+ 16. 5 4yx=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
700 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 7
Using Intercepts to Graph
Use after Section 3.3 Name ____________________________
ȿɯɚmɪlɟ: Graph.
a) 3x−2y=6
To find the y-intercept,
let 0.
x= Then solve for y:
3.0 −2y=6
−2y=6
y=−3
Thus
()
0, 3− is the y-intercept.
Plot both intercepts and a third
point
()
4, 3 as a check.
To find the x-intercept,
let 0.y= Then solve for x:
3
x
−2⋅0=6
3x=6
x=2
Thus
()
2, 0 is the x-intercept.
y
x
3x – 2y = 6
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
b) y=−3 c)
x
=4
x
y
()
,
x
y
3y=−
−2 −3
()
2, 3−−
0 −3
()
0, 3−
4 −3
()
4, 3−
x
y
()
,
x
y
x
=4
4 −2
()
4, 2−
4 0
()
4, 0
4 3
()
4, 3
y = –3
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
y
x
x = 4
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 701
EXTRA PRACTICE 7 (continued)
Using Intercepts to Graph
Use after Section 3.3
Graph.
1. 3x+6y=12 2. 2x−5y=10 3. x−3y=6
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
4. y=2 5. y=3x+1 6. 4x+2y=8
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
7. x−y=3 8.
x
=−1 9. 5x+3y=15
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
702 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 8
Slope-Intercept Form
Use after Section 3.6 Name __________________________
_
Ȱɟɟ Ȱɟɫtion 3.6 for examples.
Draw a line that has the given slope and y-intercept.
1. Ȱlɨɪɟ 4; 2. Slope 2
3; 3. Slope −5
2;
()
-intercept 0, 1y−.
()
-intercept 0, 2y
()
-intercept 0, 1y
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
4. Slope 4;− 5. Slope
1
4; 6. Slope −1
2;
()
-intercept 0, 3y
()
-intercept 0, 3y−
()
-intercept 0, 4y
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Find the slope and y-intercept of each line.
7. y=4x−2 8. y=−2
3x−4 9. y=7
4x+1
________________ ________________ ________________
10. y=−3x+2 11. y=1
5x 12. y=−x+4
________________ ________________ ________________
13. x−y=6 14. −2x+y=3 15. 3x+4y=8
________________ ________________ ________________
Extra Practice Exercises 703
EXTRA PRACTICE 8 (continued)
Slope-Intercept Form
Use after Section 3.6
Find the slope and y-intercept of each line.
16. −5x−2y=4 17. y=−3 18. 6 3 2xy+=
________________ ________________ ________________
Find the slope-intercept equation for the line with the indicated slope and y-intercept.
19. Slope
4
7; y-intercept
()
0, 5 20. Slope −2
3; y-intercept
()
0, 4−
________________ ________________
21. Slope 6 ; y-intercept
()
0, 7 22. Slope −1
8; y-intercept
()
0, 1
________________ ________________
23. Slope −5 ; y-intercept
()
0, 2 24. Slope
6
5; y-intercept
()
0, 1−
________________ ________________
Graph.
25. 2yx
=+ 26. y=−1
3x+1 27.
43
5
yx=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
28. y=−3x−1 29. y=2
3x+5 30. y=1
6x−4
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
704 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 9
Finding the Equation of a Line
Use after Section 3.7 Name ____________________________
Examples:
a) Find a slope-intercept equation for the line with slope 2 that contains
()
0, 5 .
The slope-intercept equation.
Substitute 2 for
m and 5 for b.
b) Find a slope-intercept equation for the line with slope 2 that contains
()
3, 1−.
()
11
yy mxx−= − Write the point-slope equation.
() ( )
12 3yx−− = − With
11
3, 1.xy==−
12 6yx+= − Solve for y to write a slope-intercept equation.
27yx=− This is the slope-intercept equation.
c) Find an equation of a line that contains the points
()
5, 2− and
()
2, 1−.
()
1233
25 7 7
m−−
===−
−− − First find the slope.
() ()
3
25
7
yx−− =− − Use the point-slope equation
()
11
yy mxx−= − and
substitute 3
7
− for ,m 5 for 1
x
, and 2− for 1.y
315
2
77
yx
+=− + (We could have substituted 2− for 1
x
and 1 for 1
y.)
31514
777
yx
=− + − Solve for y to write a slope-intercept equation.
31
77
yx=− + This is the slope-intercept equation.
Find a point-slope equation for a line containing the given point and having the given slope.
1.
()
4, 3 , 1m−=− ____________________ 2.
()
5, 6 , 2m−− = ____________________
3.
()
7, 2 , 3m−= ______________________ 4.
()
3, 5 , 2m=− ______________________
Find a slope-intercept equation for a line containing the given point and having the given slope.
5.
()
6, 2 , 3m−=− ____________________ 6.
()
5, 2 , 2m−= _____________________
7.
()
7, 0 , 4m= _______________________ 8.
()
0, 9 , 2m=− _____________________
9.
()
1
5, 1 , 5
m−=
______________________ 10. 1
(3, 2), 4
m−− = _____________________
y=mx +b
y=2x+5
Extra Practice Exercises 705
EXTRA PRACTICE 9 (continued)
Finding the Equation of a Line
Use after Section 3.7
Find an equation of the line that contains the given pair of points.
11.
() ( )
1, 5 and 4, 2 ___________________ 12.
() ()
4, 2 and 1, 3−− __________________
13.
()()
5, 3 and 1, 1−− − ________________ 14.
() ( )
0, 3 and 2,6− ___________________
15.
()()
8, 3 and 4,1−− _________________ 16.
() ( )
6,2 and 3,0− ___________________
17.
() ()
1, 3 and 4,6 ____________________ 18.
() ()
3, 4 and 3, 4−− __________________
19.
() ()
7,4 and 4,7−− _________________ 20.
() ()
9, 5 and 7, 7− ___________________
706 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 10
Multiplication of Polynomials
Use after Section 4.5 Name ____________________________
Examples: Multiply.
()
()
()
( )()()()
()
23
2
2
2
2
4 2 8
4 3 5 12 20
5 2 3 5 3 2 3
5 15 2 6
5 17 6
4 3 2
xxyxy
xx x x
xx xx x
xxx
xx
xx
=
−= −
++= +++
=+++
=++
−+
()()()
22
32 2
32
14 213 21
4 8 4 3 6 3
4 5 10 3
xxxx xx
xxxxx
xx x
−= + −− + −
=+−−−+
=+−+
Multiply.
1.
()()
23
35xx= ______________________ 2.
()( )
42
43xx−= _____________________
3.
()( )
35
84yy−= ____________________ 4.
()( )
()
5
234zzz−= __________________
5.
()
34 7xx−= ______________________ 6.
()
529xx−+= ______________________
7.
()
32
84 32xx x++= ________________ 8.
()
23
93 72xx x−+−= ________________
9.
()()
35xx++= ___________________ 10.
()()
7623xx++= __________________
Extra Practice Exercises 707
EXTRA PRACTICE 10 (continued)
Multiplication of Polynomials
Use after Section 4.5
11.
()()
5821xx++= __________________ 12.
()()
35xx−−= _____________________
13.
()()
37 1xx−−= ___________________ 14.
()()
6276xx−−= ___________________
15.
()
()
213xx−+= ___________________ 16.
()
()
2
24 8xx+−= __________________
17.
()
()
2
534xxx−+−= _______________ 18.
()
()
2
272xxx+−−= ________________
19.
()
()
32
43+45xxxx+− −= ___________ 20.
()()
22
37 24xx xx++ −+= ___________
21. 2
2
64
32
xx
xx
−+
++
22. 2
2
85
23
xx
x
x
−+
−−
= _____________________ = ______________________
708 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 11
Division of Polynomials
Use after Section 4.8 Name ____________________________
Examples: Divide.
a)
b)
Answer:
x3−2x2+2x+1, R −8, or
x3−2x2+2x+1+−8
x
+2
Divide.
1.
32x4−4x2
8= ___________________________________ 2. 3x5+30x3+18x
6= ______________________________
3.
y−4y2+y4
y= ___________________ 4. 27x8−15x4+3x2
x2= _________________
5.
()()
742 2
25 20 15 5xxx x−+ ÷−= 6.
()()
543 2
36 27 18 9yyy y+− ÷ =
_____________________ ____________________
7.
8r2s2+10rs3−6r2s
−2
r
s
= _______________ 8.
32 2 34
2
72135
7
x
yxyxy
xy
−+ = ____________
643 3
643
3
643
333
3
3
(15 10 35 ) (5 )
15 10 35
5
15 10 35
555
327
Answer : 3 2 7
x
xx x
xxx
x
xxx
xxx
xx
xx
−+ ÷
−+
=−+
=−+
−+
42
32
432
43
32
32
2
2
(256)(2)
221
20256
2
2 2
2 4
2 5
2 4
xxx x
xxx
xxxxx
xx
xx
xx
xx
xx
−+−÷+
−++
++−+−
+
−−
−−
+
+
6
2
8
x
x
−
+
−
Extra Practice Exercises 709
EXTRA PRACTICE 11 (continued)
Division of Polynomials
Use after Section 4.8
9.
()
()
2328 4
________________________________
xx x+− ÷−= 10.
()
()
216 64 8
________________________________
xx x−+÷−=
11.
281
9
x
x
−=
+ _________________________ 12.
2121
11
x
x
−=
− ________________________
13.
()
()
2715 5
________________________________
xx x++ ÷−= 14.
()
()
212 18 3
________________________________
xx x+−÷−=
15. 32
10 11 19 10
52
________________________________
xx x
x
−++
=
+
16. 32
12 16 27 36
34
________________________________
xx x
x
−−+
=
−
17.
()
()
42
23 1
________________________________
xx x−+÷−= 18.
()
()
42
52 2
________________________________
xx x++÷+=
19.
()()
63 3
536 4
________________________________
xx x−−÷+= 20.
()()
63 3
210 2
________________________________
xx x+−÷−=
21.
()
()
481 3
________________________________
xx−÷+= 22.
()
()
364 4
________________________________
xx−÷−=
23.
()
()
32
5 25 125 5
________________________________
aa a a−+− ÷−= 24.
()
()
32
5 25 125 5
________________________________
aa a a−+− ÷+=
710 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 12
Factoring Polynomials
Use after Sections 5.1—5.6 Name ____________________________
Examples. Factor completely.
ɚ)
()
32 2
4+12 8 4 3 2xxxxxx−= +−
b)
()()()
()
32 2 2
5 3 20 12 5 3 4 5 3 5 3 4xx x xx x x x−+ −= −+ −=− +
c)
()()
2+2 35 7 5xx x x−=+ −
d)
()()
2
35231 2xx x x−−= + −
e)
()
2
218 81 9xx x−+=−
f)
()()
22
425 2525
x
yxyxy−=+ −
g)
()
()
33 2 2
216 2 2 2 4
x
yxyxxyy+=+ −+
Factor completely. If a polynomial is prime, state this.
1. 2616xx−−= _____________________ 2. 2
472yy+−= ______________________
3. 32
52515aaa−+= _________________ 4. 2
916x−= _________________________
5. 264x−= ________________________ 6. 212 27aa++= _____________________
7. 2
6126xx++= ____________________ 8. 32
2510xxx+−−= __________________
9. 210 21xx−+= ____________________ 10. 532
12 6 3
x
xx−+= ___________________
11. 2
654y−= _______________________ 12. 2
41715yy−−= ____________________
13. 2
672xx−+= ____________________ 14. 2
55x−= __________________________
15. 53 2
3412yyy+++= _______________ 16. 2718xx−−= ______________________
Extra Practice Exercises 711
EXTRA PRACTICE 12 (continued)
Factoring Polynomials
Use after Sections 5.1—5.6
17. 2816xx−+= _____________________ 18. 2914aa−+= ______________________
19. 2
49 1x−= ________________________ 20. 43 2
8412
x
xx−+ = __________________
21. 210 25yy++= ___________________ 22. 2
3123aa+−= _____________________
23. 481x−= _________________________ 24. 2
9124yy−+= ____________________
25. 211 30aa++= ____________________ 26. 2
823tt+−= ______________________
27. 2
75 30 3xx−+= ___________________ 28. 2
383tt−−= _______________________
29. 23824xxx+++= _________________ 30. 222 121yy−+=
____________________
31. 223xx−−= ______________________ 32. 2
42436xx−+= ____________________
33. 265yy−+= _____________________ 34. 2
25 4t−= _________________________
35. 32
14 7 21
x
xx−+= _________________ 36. 2
94249xx++= ____________________
37. 3
91125x−= ______________________ 38. 2
12 4 5xx+−= _____________________
39. 2
49 28 4aa−+= __________________ 40. 2
82912xx−−= ____________________
712 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 13
Applications and Problem Solving Using Quadratic Equations
Use after Section 5.8 Name ____________________________
Example: Three times the square of a number plus five times that number is 2. Find the number.
2
Three times the square of a number plus five times that number is 2.
.
352xx
↓
↓↓ ↓ ↓↓
+=
↓
Solve:
()()
2
2
3 5 2
3520
31 20
1 2
3
xx
xx
xx
xorx
+=
+−=
−+=
==−
The values
1
3 and −2 check in the original problem. There are two numbers, 1
3 and −2.
Solve.
1. If you subtract a number from twice its square, the result is 3. Find all such numbers.
________________
2. If 6 is added to the square of a number, the result is 22. Find all such numbers. ________________
3. Five more than the square of a number is six times the number. Find all such numbers.
________________
4. Twenty more than the square of a number is twelve times the number. Find all such numbers.
________________
5. The product of the page numbers on two facing pages of a book is 600. Find the page numbers.
________________
Extra Practice Exercises 713
EXTRA PRACTICE 13
Applications and Problem Solving Using Quadratic Equations
Use after Section 5.8
6. The product of two positive consecutive even integers is 224. Find the integers. ________________
7. Two more than a number times five less than that number is 18. Find all such numbers.
________________
8. The length of a rectangle is 8 cm greater than the width. The area of the rectangle is 105 cm2. Find
the width and the length. ________________
9. The area of a square is 45 more than the perimeter. Find the length of a side. ________________
10. The height of a triangle is 6 m less than the base. The area is 56 m2. Find the height and the
base. ________________
11. The base of a triangle is 8 cm greater than the height. The area of the triangle is 120 cm2.
Find the height and the base. ________________
12. The sum of the squares of two consecutive odd whole numbers is 202. Find the numbers.
________________
714 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 14
Multiplication and Division of Rational Expressions
Use after Section 6.1 and 6.2 Name ____________________________
Examples: Find all numbers for which the rational expression x+2
x2−2x−3 is not defined.
Set the denominator equal to 0 and solve.
2
2 3 0
(3)(1)0
30 10
3 1
xx
xx
xorx
xorx
−−=
−+=
−= +=
==−
The expression is not defined when the denominator is equal to 0, or when
x
=3 or
x
=−1.
Multiply and simplify:
()
()
()
()
()()
2
2
22
44 3
44 3
92 92
22
xx x
xx x
xx xx
xx
++ −
++ −
⋅=
−+ −+
++
=
()
3x−
()()
33xx+−
()
2x+
2
3
x
x
+
=+
Divide and simplify:
()
()
()( )
()
22
22 22
2
22
22 234
16 3 4 16 2
234
16 2
2
xxx xxx
xxx xxx
xxx
xxx
x
++− ++−
÷=⋅
−+− −+−
++−
=−+−
+
=
()
4x+
()
1x−
()
4x+
()()
42xx−+
()
1x−
1
4
x
=−
Find all numbers for which the rational expression is not defined.
1.
−2
5
x
_____________________________ 2. 7
x
−3 _____________________________
3.
4
3y+2 ___________________________ 4. x2−4
5
x
−10 ___________________________
5.
x2+6
x2−3x−10 ______________________ 6. x−8
5 _____________________________
Extra Practice Exercises 715
EXTRA PRACTICE 14 (continued)
Multiplication and Division of Rational Expressions
Use after Sections 6.1 and 6.2
Multiply and simplify.
7.
8x3
5
x
⋅10
x
_________________________ 8. 5x2y
6⋅2
xy3 _________________________
9.
t2
t2−3t⋅t2−7t+12
t2−16 _________________ 10. a2−25
a2⋅a2−2a
a2+3a−10 ________________
11.
x2+8x+15
x2−1⋅x+1
x+5 __________________ 12. 10a2
4a2−a−3⋅4a−4
2a __________________
13.
6b+6
b−3⋅b2−8b+15
b2−b−2 _________________ 14. x4−81
x4−16 ⋅x2+4
x2−9 _____________________
Divide and simplify.
15. 53
84
÷ ____________________________ 16. t
4÷t
12 ____________________________
17.
a+5
a−1÷6a+30
a ____________________ 18. x2−49
x
÷x+7
x
−2 _____________________
19.
x2−64
2
x
+16 ÷x−8
5 ____________________ 20. a+b
3a÷a2−b2
9a3 _____________________
21.
c2+4c
c2−c−20 ÷c
c−5 __________________ 22. 3y2+y−2
3y2−8y+4÷y2−y−56
y2+5y−14 ____________
23.
x2+10x+21
x2+5x+4÷x3+7x2
x2+4x _____________ 24. 5t2−50t−40
10t−40 ÷t2−5t−14
t2−8t+7 ____________
716 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 15
Addition and Subtraction of Rational Expressions
Use after Sections 6.3 and 6.4 Name ____________________________
Example: Do this calculation.
()()()() ()()()
()() ()()
()()
()()()
()()()
()()()
()
22
22
2
52
34 68
52
,LCM 4 2 1
41 42
5221
41 2 42 1
5221
421
5102 2
421
312
421
34
xx
xx xx
xx xxx
xx xx
xx xx
xxx xx x
xx xx
xxx
xxxx
xxx
xx
xxx
xx
−
−− −+
=− =−−+
−+ −−
−+
=⋅−⋅
−+− −− +
−− +
=−−+
−−−
=−−+
−
=−−+
−
=
()
4x−
()()
()()
21
3
21
xx
x
xx
−+
=−+
Add or subtract. Simplify.
1.
x−1
x
+3+x+7
x
+3 ______________________ 2. x−1
x
+6+x+3
x
−2 _______________________
3.
a2
a−4+16
4−a ______________________ 4. 4y
y2−y−2−5y
y2+y−6 _______________
5.
3x+2
x
−1−x+5
x
−1 _____________________ 6. 4
a+2+a+1
a2−4−3
a−2 ________________
7.
y−5
3y+9−y+1
2y+6 ____________________ 8. 5
a+3
−a ___________________________
9.
x+1
x2−7x+10 +3
x2−x−2 _____________ 10. b−3
b2−9+b+3
b2+6b+9 __________________
Extra Practice Exercises 717
EXTRA PRACTICE 15 (continued)
Addition and Subtraction of Rational Expressions
Use after Sections 6.3 and 6.4
11.
a−5
a2−5a+a+5
a2−25 __________________ 12. y+7
y2−49 −3y+1
49 −y2 ___________________
13.
x+2
x2+x−1
x+3
x+1 __________________ 14. b+3
2b+6−2
3b ________________________
15.
5x
x+2−x
x−1+3
x2+x−2 16. 5
x2+3x−4
x2−x−12
_________________________________ __________________________________
17. 2
35
111
aa
aa a
+−
−+ −
18. 8x+4
2x2−9x−5+x−1
x−5
_________________________________ __________________________________
19.
y−5
6y−4y+1
y _____________________ 20. 9x
x2−81 +3x
x+9 _____________________
718 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 16
Simplifying Complex Rational Expressions
Use after Section 6.5 Name ____________________________
Example: Simplify.
()
()()
2
2
22
22
22
2
2
2
11
33
11
99
1
3
1
9
3
91
31
3131
31
x
xx
x
xx
x
x
x
x
x
x
xx
x
xx
xx
x
x
−−
=⋅
−−
⋅−⋅
=
⋅− ⋅
−
=−
−
=−+
=+
or
()()
2
222
2
2
2
2
2
11
33
11
99
31
91
31
91
31
3131
31
x
xxx
x
xxx
x
x
x
x
xx
xx
xx
xx x
x
x
−⋅−
=
−⋅−
−
=−
−
=⋅
−
−
=⋅
−+
=+
Simplify.
1.
4
19
2
13
+
−
____________________________ 2.
88
27
11
3
−
+
___________________________
3.
14
12
x
x
+
−
___________________________ 4.
4
4
a
a
aa
+
+
____________________________
5.
11
12
x
x
−
−
___________________________ 6.
32
3
3
yy
y
y
+
+
___________________________
Extra Practice Exercises 719
EXTRA PRACTICE 16 (continued)
Simplifying Complex Rational Expressions
Use after Section 6.5
7.
2
1
1
1
1
x
x
−
−
___________________________ 8.
1
4
4
x
x
−
____________________________
9. 2
22
a
ab
a
ab
+
−
_________________________ 10.
11
x
y
x
y
yx
+
−
____________________________
11.
3
2
43
25
mm
mm
+
−
_________________________ 12.
3
3
31
42
35
24
x
x
x
x
−
+
_________________________
13.
11
8
8
8
y
y
−
− ___________________________ 14.
4
4
9
2
3
x
x
x
−
+
___________________________
15.
3
2
4
28
a
a
aa
−
−
__________________________ 16.
22
32
43
21
x
yxy
x
yxy
+
+
________________________
720 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 17
Solving Rational Equations
Use after Section 6.6 Name ____________________________
Example: Solve.
5
x
+2=3
x
The LCM is
()
2.xx+
() ()
()
53
22
2
5 3 2
5 3 6
26
3
xx xx
x
x
xx
xx
x
x
§· §·
+=+
¨¸ ¨¸
+
©¹ ©¹
=+
=+
=
=
The solution is 3.
Check: 5
x
+2=3
x
5
32+ 3
3
5
5 1
1 1
Solve.
1.
4
x
−1=5
x
_________________________ 2. x−3
x
+2=4
5 _________________________
3.
5
x
=4
x
+1
2 ________________________ 4. 1
3−3
4=x
12 ________________________
5.
4
3
x
+2
x
=2
3 _______________________ 6. 8
x
−5=2
x
+5 _______________________
7.
x−7
x
+3=2x
x
+3 ______________________ 8. y−1
4−y+1
10 =1 _____________________
TRUE
?
Extra Practice Exercises 721
EXTRA PRACTICE 17 (continued)
Solving Rational Equations
Use after Section 6.6
9.
a+3
a=5 _________________________ 10. 32bb
−= _________________________
11.
1
x
−4
x
+5
x
=1
4 _____________________ 12. x−2
x
+2=x+10
x
______________________
13.
x+5
x
=6 _________________________ 14. 2x
x−6−1
x+6=27
x2−36 _______________
15.
x−2
x
=4−x+4
x
−3 ___________________ 16. 2x+1
5
x
−3=5x+1
6
x
−2 _____________________
17.
2x−1
5−x+2
15 =1 ___________________ 18. x+3
x
−1=x+2
x
−3 _______________________
722 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 18
Applications Using Rational Equations and Proportions
Use after Section 6.7 Name ____________________________
Example: A number plus five times its reciprocal is −6 . Find the number.
A number plus five times its reciprocal is 6.
1
5. 6xx
−
↓↓↓ ↓
+=−
↓↓
Solve:
x+5⋅1
x
=−6
()
()()
2
2
56 Multiplying by the LCD, , on both sides.
5 6
6 5 0
510
5 1
xx x x
x
xx
xx
xx
xorx
§·
+=−
¨¸
©¹
+=−
++=
++=
=− = −
The values í5 and í1 check in the original problem. The solutions are í5 and í1.
Solve.
1. A number minus three times its reciprocal is 2. Find the number. ________________
2. The sum of a number and twice its reciprocal is 3. Find the number. ________________
3. It takes Carolyn 4 hr to type a final exam. It takes Elise 3 hr to do the same job. How long
would it take them, working together, to do the typing? ________________
4. A swimming pool can be filled in 15 hr by pipe A alone and in 24 hr by pipe B alone. How
long would it take to fill the pool if both pipes were working? ________________
5. One car travels 30 km/h faster than another. In the same time that one car travels 200 km, the
other car goes 320 km. Find their speeds. ________________
Extra Practice Exercises 723
EXTRA PRACTICE 18 (continued)
Applications Using Rational Equations and Proportions
Use after Section 6.7
6. The speed of a freight train is 16 mph slower than the speed of a passenger train. The freight train
travels 420 miles in the same time that it takes the passenger train to travel 500 miles. Find the speed
of each train. ________________
7. William walked 195 km in 12 days. At this rate, how far would he walk in 36 days?
________________
8. The winner of an election for class president won by a vote of 8 to 5 with 992 votes. How many
votes did the loser get? ________________
9. Triangles
A
B
C
and
X
Y
Z
are similar. Solve for z if
x
=12 , a=10 , and c=8.
________________
10. Triangles
D
E
F
and G
H
I
are similar. Solve for e if d=15, g=9 , and h=6.
________________
11. To determine the number of deer in a game preserve, a game warden catches 415 deer, tags
them, and lets them loose. Later, 140 deer are caught; 28 of them are tagged. Estimate the
number of deer in the preserve. ________________
724 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 19
Functions
Use after Sections 7.1 and 7.3 Name _________________________
_
Examples.
Given
( ) ( )
( ) ( )
3 7, find 2 .
2 3 2 7 6 7 13
f x x f
f
=− −
−=− − =− − =−
Given
( ) ( )
( ) ( ) ( )
2
2
2 5 2, find 0 .
0 2 0 5 0 2 2 0 5 0 2 2
f x x x f
f
=−+
=−+ = ⋅ − ⋅ + =
Find the indicated function values.
1.
( )
2 5f x x= +
a)
( )
2f−= __________________
b)
( )
8f−= _________________
c)
( )
0f= ___________________
d)
( )
1.2f= _________________
e) 3
4
f! ” =
# $
% & __________________
3.
( )
22h x =−
a)
( )
11h−= _________________
b)
( )
1.6h−= ________________
c)
( )
0h= ___________________
d)
( )
15h= __________________
e)
( )
209h= _________________
5.
( )
2g t t=−
a)
( )
7g= ___________________
b)
( )
5g−= __________________
c)
( )
30g−= _________________
d)
( )
400g= _________________
e)
( )
1g a + = ________________
2.
( )
25g t t=−
a)
( )
0g= __________________
b)
( )
7g= __________________
c)
( )
9g−= _________________
d)
( )
1.4g−= _______________
e) 2
3
g! ” =
# $
% & _________________
4.
( )
8f x x=−
a)
( )
19f−= ________________
b)
( )
1f−= _________________
c)
( )
0f= __________________
d)
( )
18f= _________________
e)
( )
100f= ________________
6.
( )
3
2
f
x x x=−
a)
( )
0f= __________________
b)
( )
4f= __________________
c)
( )
3f−= _________________
d)
( )
4
f
a= _________________
e)
( )
10f−= ________________
Extra Practice Exercises 725
EXTRA PRACTICE 19 (continued)
Functions
Use after Sections 7.1 and 7.3
Graph each function.
7.
( )
4 2f x x= + 8.
( )
3 1
f
x x=− − 9.
( )
24
3
g x x=−+
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
10.
( )
12
4
f x x=− 11.
( )
2h x x=− 12.
( )
3
f
x x=
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
Determine whether the graph is that of a function.
13. 14. 15.
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
y
x
–5 –2 –1
–1
1
2
3
4
5
–2
–3
–5
–3– 4
–4
1 2 34 5
_____________________ _____________________ _____________________
726 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 20
Solving Systems of Linear Equations
Use after Section 8.2 Name ____________________________
ȿɯɚmɪlɟs:
a) Solve using the substitution method: 52 4,
5.
xy
yx
−=
=−
Substitute
5−
x
for y.
5 2 4
52(5)4
5102 4
7 14
2
xy
xx
xx
x
x
−=
−−=
−+ =
=
=
Then substitute 2 for
x
and solve for y.
y=5−
x
y=5−2
y=3
The solution is
()
2, 3 .
b) Solve using the elimination method: 2x+7y=−1,
−x−2y=2.
Multiply the second equation
by 2 and then add.
2 7 1
24 4
3 3
1
xy
xy
y
y
+=−
−− =
=
=
Then substitute 1 for y and solve for
x
.
27 1
2711
271
2 8
4
xy
x
x
x
x
+=−
+⋅=−
+=−
=−
=−
The solution is
()
4, 1 .−
Solve.
1. 431,
1
x
y
x
y
+=
=− ______________________ 2. 2x−y=6,
−x+y=−1 ________________________
3.
6
x
−y=3,
4x−2y=−2 _____________________ 4. 2
x
+3y=7,
x=1−4y ________________________
5.
2
x
+3y=6,
x−3y=−15 _____________________ 6. 75 4,
34
x
y
yx
−=
=− _______________________
Extra Practice Exercises 727
EXTRA PRACTICE 20 (continued)
Solving Systems of Linear Equations
Use after Section 8.2
7.
25 1,
25
yx
xy
−=−
=+ ____________________ 8. 431,
35 13
x
y
xy
+=
+=− _____________________
9. 653,
43 21
x
y
xy
−=
+= _____________________ 10. 4,
3410
x
y
xy
+=
+= _______________________
11. 32,
781
x
y
xy
−+=
−=
_____________________ 12. 722,
214
x
y
xy
+=
−= _______________________
13. 92 7,
35
yx
xy
−=−
−= ____________________ 14. 35 8,
4712
x
y
xy
−=
−=
_______________________
15. 5212,
34 2
x
y
xy
+=
−= ____________________ 16. 47,
37 6
x
y
xy
+=
+=
_______________________
17. 58 25,
47
x
y
xy
−=
−+ =− ____________________ 18. 0.5
x
+2y=9,
4x−1.5y=2 _______________________
19.
860,
13
94
xy
xy
−=
+= ______________________
20.
2
3x+1
4y=18,
1
6x−3
8y=−6
______________________
728 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 21
Solving Applications: Systems of Two Equations
Use after Section 8.3 Name ____________________________
Example: The campus bookstore sells two kinds of sweatshirts. The hooded ones sell for $39.50 and
the crewneck ones sell for $34.50. During the first week of school, a total of 250
sweatshirts were sold at a total value of $9185. How many of each kind were sold?
We let
x
represent the number of hooded sweatshirts sold and y represent the number of
crewneck sweatshirts sold.
The total sold was 250, so we have 250.xy+= The total amount taken in was $9185, thus
we have 39.50x+34.50 y=9185 .
We solve the following system.
x+y=250
39.5x+34.5y=9185 or
()
250
395 345 91,850 Multiplying by 10
xy
xy
+=
+=
The solution of the system is
x
=112 and 138.y= These values check. Thus 112 hooded
sweatshirts and 138 crewneck sweatshirts were sold.
Solve.
1. The sum of two numbers is 11.−Twice the first number minus the second is 32. Find the numbers.
________________
2. Two investments are made totaling $16,000. For a certain year these investments yield $970 in
simple interest. Part of the $16,000 is invested at 5% and the rest at 7%. How much is invested at
7%? ________________
3. A collection of nickels and dimes is worth $3.30. There are 42 coins in all. How many of each kind
of coin are there? ________________
4. Patrick is 4 years younger than his sister Alice. In five years, Patrick will be
3
4
as old as Alice. How
old is Patrick now? ________________
5. The difference between two numbers is 14. Twice the smaller is 7 more than the larger. What are the
numbers? ________________
6. The perimeter of a lot is 84 ft. The length exceeds the width by 16 feet. Find the length and the width.
________________
Extra Practice Exercises 729
EXTRA PRACTICE 21 (continued)
Solving Applications: Systems of Two Equations
Use after Section 8.3
7. One night a theater sold 548 movie tickets. An adult’s ticket costs $6.50, and a child’s ticket costs
$3.50. In all, $2881 was taken in. How many of each kind of ticket were sold? ________________
8. A train leaves Smithville and travels south at a speed of 60 mph. Three hours later, a second train
leaves on a parallel track and travels south at 90 mph. How far from the station will they meet?
________________
9. The sum of a certain number and a second number is 21. The second number minus the first number
is –57. Find the numbers. ________________
10. The perimeter of a rectangular field is 110 feet. The length is 7 feet more than twice the width. Find
the dimensions. ________________
11. A chemist has one solution that is 20% saline and a second that is 65% saline. How many gallons of
each should be mixed together to get 120 gallons of a solution that is 50% saline?
________________
12. Two investments are made totaling $23,000. For a certain year these investments yield $2095 in
simple interest. Part of the $23,000 is invested at 8% and the rest at 11%. How much is invested at
each rate? ________________
13. Two angles are complementary. One angle is 10° less than three times the other. Find the measures
of the angles. ________________
14. A small boat took 2 hr to make a trip downstream with a 4-mph current. The return trip against the
same current took 3 hr. Find the speed of the boat in still water. ________________
730 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 22
Solving Systems of Equations in Three Variables
Use after Sections 8.4 and 8.5 Name ____________________________
See Sections 8.4 and 8.5 for examples of both solving systems of equations in three variables and
applications.
Solve each system. If a system’s equations are dependent or if there is no solution, state this.
1. 23 9,
243 16,
4313
_________________
xyz
xyz
xy z
−+=−
−+=−
+− =
4. 738144,
221,
2 8 7 105
_________________
xxz
yz
xyz
++=
+=
++=
7. 750,
32 40,
23 8
_________________
yz
xz
xyz
−=
−−=−
−−=
10. 983 43
814,
8663
_________________
xyz
xyz
xy z
−−=−
+−=
−−−=−
13. 982 8,
5424,
766
_________________
xyz
xyz
xy
−+−=−
−−=
−=
16. 18 16 15 158,
68986,
36 32 30 79
____________________
xyz
xyz
xyz
−+=
−++=
−+−=−
2. 411,
34 7,
52219
_________________
xyz
xy
xyz
++=
+=
++=
5. 67 39,
32 6,
595 36
_________________
xyz
xy
xyz
−+=−
−=
−+=−
8. 38929,
6651,
25518
_________________
xyz
xyz
xyz
−+−=
−+−=
−+−=
11. 63,
9,
48472
_________________
yz
xyz
xyz
−=
−−+=−
+−=
14. 37 27,
6545,
4460
_________________
yz
xy z
xyz
−−=−
−+−=−
−+−=
17. 3 14 8 27,
19 15 17 211,
2432
___________________
xyz
xyz
yz
−+=
−++=
−+=
3. 32229,
989116,
2986
_________________
xyz
xyz
xyz
++=
++=
++=
6. 55 8,
53 8,
9831
_________________
xyz
xyz
xy z
−++=
−++=−
−++=−
9. 29552,
84448,
54337
_________________
xyz
xyz
xyz
−−+=
−−+=
−−+=
12. 37 43,
639 24,
6666
_________________
xyz
xyz
xyz
−−−=−
+−=−
−−+=
15. 8734,
67449,
21614 68
_________________
xyz
xyz
xyz
++=
++=
++=
18. 685 6,
298 88,
88980
_________________
xyz
xyz
xyz
−+−=−
−−=−
−−+=
Extra Practice Exercises 731
EXTRA PRACTICE 22 (continued)
Solving Systems of Equations in Three Variables
Use after Sections 8.4 and 8.5
Solve.
19. The sum of 3 numbers is 22. The third is 2 more than twice the second. The first is twice the second.
Find the numbers. ________________
20. The sum of 3 numbers is 8. The second is 5 more than twice the third. The first is three times the sum
of the second and third. Find the numbers. ________________
21. The sum of 3 numbers is 12. Twice the first plus the second is twice the third. Three times the second
plus the first is 3 times the third. Find the numbers. ________________
22. The third of 3 numbers is 27 less than twice the second. The first and the third differ by 2 more than
the second number. Twice the first is the same as the second minus the third. Find the numbers.
________________
23. The sum of 3 numbers is 8. Twice the first is one more than the second. The third is 5 less than 1
2
the
first. Find the numbers. ________________
24. In triangle ,
A
BC angle C is 20° more than angle .
A
Angle
B
is twice the sum of angles
A
and
.C Find the angles. ________________
25. In triangle ,
A
BC angle
B
is 2° less than twice angle .
A
Angle C is 7° more than twice angle .
A
Find the angles. ________________
26. In triangle ,
X
YZ angle Y is 11° less than twice angle .
Z
Angle Y is 23° less than three times angle
.
X
Find the angles. ________________
27. Albert, Beth, and Cathy can fold 460 napkins in an hour. Albert and Cathy can fold 247 in an hour.
Cathy and Beth can fold 310 in an hour. How many napkins can each person fold individually in an
hour? ________________
28. John bought 3 types of donuts: apple, blueberry, and chocolate. He bought one for every person in a
class of 30 people. John realized that most people like chocolate, so he bought as many chocolate as
the other two types combined. Apple donuts cost 70¢ a piece, blueberry cost 75¢ a piece, and
chocolate cost 80¢ a piece. John spent a total of $22.85. How many of each type did he buy?
________________
732 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 23
Solving Inequalities
Use after Section 9.1 Name ____________________________
Examples: Solve.
a)
()
4 6 10
446 4 10
6 14
11
( 6 ) ( 14)
66
14
6
7
3
x
x
x
x
x
x
−<−
−+− <−+−
−<−
−⋅− >−⋅−
>
>
77
The solution set is | , or ,
33
xx
½§·
>−∞
®¾
¨¸
¯¿©¹
b)
()
7 4 5 12
7445124
7 5 8
57 558
2 8
11
2 8
22
4
yy
yy
yy
yy yy
y
y
y
−≥ −
−+ ≥ − +
≥−
−+ ≥−+−
≥−
⋅≥⋅−
≥−
{
}
[
)
The solution set is | 4 , or 4, .yy≥− − ∞
Solve.
1. 4723x+≤ _______________________ 2. 3 4 8 5yy+≥ − _____________________
3. 12 5 3 7yy+< − ___________________ 4. 0.7 1.4 0.3
x
x<− ____________________
5. 32055
x
xx+−≥+ ________________ 6. 5 3 7y−+<− _______________________
7. 14 5 2 3xx−>+ ___________________ 8. 3 10 8 5yy−≤ − ____________________
9. 144
2y−< _______________________ 10. 2 2yy−>+ _______________________
Extra Practice Exercises 733
EXTRA PRACTICE 23 (continued)
Solving Inequalities
Use after Section 9.1
11. 7464xx−≤ + ____________________ 12. 55 8 1y≥− ________________________
13. 3225x−+>− _____________________ 14. 1
829
2
yy−+ ≤− ___________________
15. 0.3 0.8 11yy>− ___________________ 16. 21
22
33
x
x−<− ____________________
17. 8 0.9 0.1x+≤− ____________________ 18. 0.4 3 2y−≥ _______________________
19. 6 4 16y−> _______________________ 20. 8 5 4xx−≤+ ______________________
21. 7 0.3 0.3 2yy−≤− _________________ 22. 15 7 18 5xx−− > ____________________
23. 372
x
≥− ________________________ 24. 11 3
23
88
x
x−<− ____________________
25. 18 5 4 7xx−<−
___________________ 26. 13
2
22
y≥− ________________________
27. 29 11 4x>− ______________________ 28. 7 7yy−≤− _______________________
29. 4.3 14 72y−−< ___________________ 30. 32
48
55
xx−≥ + ____________________
734 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 24
Solving Equations and Inequalities with Absolute Value.
Use after Section 9.3 Name ____________________________
Examples: Solve.
a) 3 5 16
3 5 16 3 5 16
3 11 3 21
11
7
3
11
The solution set ,7 .
3
x
xorx
xorx
xorx
−=
−=− −=
=− =
=− =
½
−
®¾
¯¿
b) 3 5 16
16 3 5 16
11 3 21
11
7
3
11 11
The solution set is 7 , or ,7 .
33
x
x
x
x
xx
−≤
−≤−≤
−≤ ≤
−≤≤
½
ªº
−≤≤ −
®¾
«»
¬¼
¯¿
c)
()
3 5 16
3 5 16 3 5 16
3 11 3 21
11
7
3
11 11
The solution set is | 7 , or , 7, .
33
x
xorx
xorx
xorx
xx orx
−>
−<− −>
<− >
<− >
½§·
<− > −∞ − ∪ ∞
®¾
¨¸
¯¿©¹
Solve.
1. 8321x−> ______________________ 2. 27y−≤ _________________________
3. 5823x+< ______________________ 4. 92 5x−= _______________________
5. 4x= __________________________ 6. 133
2y−≥
_______________________
7. 92y+≤ _______________________ 8. 14
33
y+>
________________________
9. 4313x−+> ____________________ 10. 510
8x< ________________________
Extra Practice Exercises 735
EXTRA PRACTICE 24 (continued)
Solving Equations and Inequalities with Absolute Value
Use after Section 9.3
11. 10 1.3 4.7y−= __________________ 12. 94 15x−≥ _______________________
13. 917x+> _______________________ 14. 31
44
x+=
_______________________
15. 911y−> _______________________ 16. 1
5
y≤ ___________________________
17. 33
77
y> _______________________ 18. 32x−= ________________________
19. 5215x−≥ ______________________ 20. 17 4 23x−< _____________________
21. 351y−= _______________________ 22. 19 19x−> _______________________
23. 835x−≤ ______________________ 24. 2915y−< ______________________
25. 9y> __________________________ 26. 54
399
y−≤
_______________________
27. 83 35y−< _____________________ 28. 0.2 0.5 0.9x+≥ ___________________
29. 24
99
x−≥
_______________________ 30. 34 4 14y−≤ _____________________
736 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 25
Inequalities in Two Variables
Use after Section 9.4 Name ____________________________
Examples: Graph.
a) 5y<
y
y < 5
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
b) 3xy+≥
y
x + y ≥ 3
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Determine if the given ordered pair is a solution to the inequality.
1.
()
3, 6 ; 2 3 8xy+> ______________ 2.
()
1, 4 ; 2 6 < 19xy−+ ___________
3.
()
3, 8 ; 4 8 20xy−−> ___________ 4.
()
1, 3; 6310xy+> _____________
5.
()
1, 11 ; 4 3 29xy−<− ___________ 6.
()
6, 7 ; 3 9 25xy−+ > ____________
Graph.
7. ( 2y< 8.
3x> 9. 4y≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 737
EXTRA PRACTICE 25 (continued)
Inequalities in Two Variables
Use after Section 9.4
10. 4x≤ 11. 3yx<+ 12. 5yx≤−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
13. 6yx>+ 14. 3 2xy≤+ 15. 2 3 5xy+≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
16. 2 5 13yx−< 17.
53x−≤ < 18. 3 4xy−≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
738 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 25 (continued)
Inequalities in Two Variables
Use after Section 9.4
19. 437xy+≥ 20. 2 4y<≤ 21. 4 2 3
x
yx+≤ +
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Graph each system.
22. 4;
5
y
yx
≥
≤+ 23. 2;
3
yx
x
y
<+
< 24. 32;yx
yx
>+
<
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
25. 523;
234
x
y
xy
+>
−≤
26. 34;
2
yx
yx
≥
>− 27. 43;
32
x
y
y
+<
≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 739
EXTRA PRACTICE 25 (continued)
Inequalities in Two Variables
Use after Section 9.4
28. 63 2;
0
x
y
x
+≤ +
≥ 29. 0;
33
x
y
yx
+>
<+
30. 435;
53
x
y
xy
+<
≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Graph the system. Find coordinates of any vertices formed.
31.
22;
52;
3
yx
yx
x
≥+
≤−
≥
32.
93;
5;
2
yx
x
xy
≤−
≤
≥+
33.
314;
324;
4
xy
yx
xy
+≤
+≥
+≥
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
34.
32 4;
327;
01
xy
xy
x
+≥
+≤
≤≤
35.
523;
254;
0;
0
xy
yx
x
y
+≥
−≤
≥
≥
36.
326;
3210;
2;
5
xy
xy
x
y
+≥
+≤
≥
≤
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
740 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 26
Radical Expressions and Rational Numbers as Exponents
Use after Sections 10.1 and 10.2 Name ____________________________
Examples: a) Given
()
316fx x=−
, find
()
7f and
()
3f.
()
()
7371621165
33316916 7
f
f
=−=−=
=−=−=−
<
<
Since
7− is not a real number, we say 7−does not exist.
b) Rewrite
()
1/ 4
32
ab using radical notation.
()
1/ 4
32 324
ab ab=
c) Simplify:
21
34
x
x⋅.
218311
11
12
34 121212
x
xxxx x⋅=⋅ ⋅ =
For each function, find the function value if it exists.
1.
() () () () ( )
3 5; 2, 6, 9, 2fx x f f f f=+ − ___________________________
2.
() () ( ) () ()
6 10; 4, 6, 5, 3fx x f f f f=− − __________________________
3.
() () ( ) () ( )
48; 2, 2,3, 3fx x f f f f=+ − − __________________________
4.
() () ( ) () ()
356; 2, 6,3, 8fx x f f f f=+ − ____________________________
5.
() ()()() ()
364; 1,3,4, 6fx x f f f f=− − − __________________________
6.
() () ( ) () ()
42 3; 0, 2, 1, 2gx x g g g g=+ − ___________________________
Simplify. Assume that variables can represent any real number.
7.
()
2
5− ______________ 8. 2
16
x
_______________ 9. 3
81
x
_______________
10. 33
343
x
______________ 11. 33
64z _______________ 12.
()
327− _____________
13.
()
7
7z− ______________ 14. 2
4129xx++ ________ 15.
()
2
23x+ _________
16.
()
13
13 6
x
− ____________ 17. 3216
343 _______________ 18. 3125
729
− ___________
19. 7128
2187 ______________ 20.
()
5
54ab _____________
Extra Practice Exercises 741
EXTRA PRACTICE 26 (continued)
Radical Expressions and Rational Numbers as Exponents
Use after Sections 10.1 and 10.2
Find the domain of each of the following functions.
21.
()
3fx x=− _______________________
23.
()
9fx x=− _______________________
25.
()
4
35fx x=+ − ____________________
22.
()
25fx x=+ ______________________
24.
()
335fx x=− ______________________
26.
()
223fx x=+ + ___________________
Assume for all exercises that even roots are of non-negative quantities and that all denominators
are nonzero.
Rewrite using radical notation. Simplify, if possible.
27. 16
y _________________ 28. 12
4 _________________ 29. 15
32 _______________
30. 32
16 ________________ 31.
()
16
x
y _______________ 32.
()
12
169
x
___________
33. 53
64 ________________ 34.
()
1
23
8
x
yz ____________ 35.
()
34
625 ____________
Rewrite using exponential notation.
36. 316 ______________ 37. 52
x
_________________ 38. 2
3
x
y ______________
39.
()
3
4
x
y ___________ 40. 3
410ab ______________ 41.
()
3
52
abc ___________
42. 22
4
x
y ____________ 43. 23
3
x
y ______________ 44. 325
5
x
yz ___________
Simplify. Write answers using radical notation.
45. 34
y− _________________ 4 6.
()
3
22
10xy− __________ 47.
12
1
64
−
§·
¨¸
©¹ ____________
48.
23
5
6
a
bc
−
§·
¨¸
©¹
__________ 49.
32
25
x
x
−
− _______________ 50. 2
15
2
x
x⋅ ____________
51.
()
1
52
3
3
2
xy
−⋅ _________ 52.
()
1
53
6
x _____________ 53.
()
1
314
52
ab⋅ ________
54. 31
55
6 6⋅ __________ 55. 23
52
4 4
−
⋅ ______________
742 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 27
Multiplying, Dividing, and Simplifying Radical Expressions
Use after Sections 10.3 and 10.4 Name ____________________________
Examples. Simplify. Assume that all variables represent positive numbers.
a) 642
3
63 2
3
63 2
33
22
3
320
64 5
64 5
4 5
xyz
x
yyz
xy yz
xy yz
=⋅⋅⋅⋅⋅
=
=
b)
()
()
()
2
84
4
2
484
4
2
2
42
81
= 3
= 3
= 9
ab
ab
ab
ab
c) 5
2
5
2
4
2
2
75
16
75
=
16
25 3
=
16
53
= 4
y
x
y
x
yy
x
yy
x
⋅
Simplify. Assume that all variables represent positive numbers.
1. 32
20
x
yz = _______________________ 2. 42
3128
x
y= ________________________
3. 16 124ab = _________________________ 4.
3
4
49a
b= __________________________
5. 32
45abc = _______________________ 6. 3
16 = ____________________________
7.
5
36
16
x
y= _________________________ 8. 712
464ab = ________________________
9. 25
50ab = ________________________ 10.
()
3
10
532x= ________________________
11.
3
16
81
x
= _________________________ 12. 211
500
x
yz = _______________________
13. 32
216 = _________________________ 14.
7
364
27
a= __________________________
15. 45
3240
x
y= _______________________ 16. 7912
4
x
yz = _________________________
17.
3
24
25
x
= _________________________ 18. 3
4256 = ___________________________
19.
()
3
510
532ab = _____________________ 20.
()
2
3
354a= ________________________
Extra Practice Exercises 743
EXTRA PRACTICE 27 (continued)
Multiplying, Dividing, and Simplifying Radical Expressions
Use after Sections 10.3 and 10.4
Examples. Assume that all variables represent positive numbers.
a) Multiply and simplify.
325
38
28
28
4
32 4
128
64 2
64 2
82
xy x y
xy
x
xy
xy x
xy x
=
=⋅⋅⋅⋅
=
=
b) Divide and simplify.
3514
35
514
3
5
349
393
3
3
56
7
56
7
8
8 2
ab
ab
ab
ab
ab
aab aba
=
=
=⋅⋅⋅=
Multiply or divide and simplify. Assume that all variables represent positive numbers.
21.
() ()
22
33
52252xx++
= ____________ 22.
53
2
32
2
ab
ab
= _________________________
23.
3
645
35
x
x
= ________________________ 24. 372
364
x
xy = ______________________
25. 32
83
x
yxy= ____________________ 26.
358
32
81
3
ab
ab
= _________________________
27.
64
3
3
625
5
x
y
x
y = ______________________ 28.
()()
3
6333xx++= _______________
29. 33
52 2
66ab ab= ___________________ 30.
7
3
3
27
x
y
x
y= _________________________
31.
811
5
2
5
9160
35
x
y
xy
= _____________________ 32.
()()
25
33
4323yy−−= ______________
744 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 28
Solving Radical Equatiɨns
Use after Section 10.6 Name ____________________________
Example: Solve.
()()
()
22
2
2
19 20 3
19 20 3
19 20 3
19 20 6 20 9
30 6 20
520
520
25 20
45
xx
xx
xx
xx x
x
x
x
x
x
+− −=
+= −+
+=−+
+=−+ − +
=−
=−
=−
=−
=
Check:
19 20 3
45 19 45 20 ?3
64 25
8 5
3
xx+− −=
+− −
−
−TRUE
The solution is 45.
Solve.
1. 272xx+= + ____________________ 2. 33x−= _________________________
3. 927xx++ += ________________ 4. 53yy−= − ______________________
5. 342
x
x−+=− ___________________ 6. 151
x
x−=− + _____________________
7. 25a+= ________________________ 8. 5611xx−+ += _________________
Extra Practice Exercises 745
EXTRA PRACTICE 28 (continued)
Solving Radical Equatiɨns
Use after Section 10.6
9. 3130x−−= ______________________ 10. 3281yy+− −=
_________________
11. 12 12 12xx+− −= ______________ 12. 4291xx+− +=−
________________
13. 7411xx++ −= ________________ 14. 51x−= _________________________
15. 34325x++= ____________________ l6. 945xx++ += __________________
17. 10 3xx++ = ___________________ 18. 53 37xx+= + ___________________
19. 78 412 3xx+− − = ______________ 20. 10 2 5 16 3xx−− += ______________
746 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 29
The Pythagorean Theorem and special Triangles
Use after Section 10.7 Name ____________________________
See Section 10.7 for examples.
Find the length of the missing side. Give an exact answer.
1. 3, 4ab== _______________________ 2. 5, 12ab== _______________________
3. 15, 17ac== _____________________ 4. 12, 18bc== _______________________
5. 5, 5 2ac== _____________________ 6. 9, 17ac== _______________________
7. 3, 4bc==
_______________________ 8. 10, 10ab==
______________________
9. 8, 14ac== ______________________ 10. 6, 12bc== _______________________
Give an exact answer.
11. Ⱥ wire reaches from the top of a 20-ft pole to a point 7 feet from its base. How long is the wire?
________________
12. John is in one corner of a 12 ft ×15 ft room. His brother is in the opposite corner. John throws a ball
to his brother. How far does he have to throw it? ________________
13. Jim starts at post A in a corn field. He heads directly south 10 feet, then east 12 feet, to
post .C He then turns south 18 feet from C and east another 4 feet, where he reaches
post .
B
What is the shortest distance between posts A and
B
if he must pass C on the way?
________________
14. A 19″ T.V. set (measured on the diagonal) has a width of 8 inches. What is its height?
________________
For each of the following, find the missing length(s). Give exact answers. (Drawings not to scale.)
15. _____________________ 16. ______________________
Extra Practice Exercises 747
EXTRA PRACTICE 29 (continued)
The Pythagorean Theorem and Special Triangles
Use after Section 10.7
17.
45°
_______________ 18. ________________________
19. ________________________ 20.
30°
________________
21.
60°
________________________ 22. ___________________
23. _______________ 24. ___________________________
25. In this square, what is the distance between A and B? ____________
26. Alex knows that Ⱥɪɪleville is 30 miles due east of Bakersfield. Carpentersville is 40 miles south of
Appleville. How far is it from Bakersfield to Carpentersville? ________________
27. What is the perimeter of a square that has a diagonal of 2 meters? ________________
28. A rectangle has one side 2 ft longer than another. The diagonal is 10 ft. What is the perimeter?
748 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 30
Solving Quadratic Equations Using the Quadratic Formula
Use after Section 11.2 Name ____________________________
Example: Solve 2
5820xx−+= using the quadratic formula.
2
5820xx−+=
5 8 2ab c==−=
() () ()()
()
()
2
88452
25
86440824
10 10
24 6
826 4 6
10 2 5 5 5
x−− ± − −
=
±− ±
==
±
±
== =±
⋅
2
Quadratic Formula:
4
2
bb ac
xa
ªº
«»
−± −
«»
=
«»
¬¼
Solve.
1. 2
5480xx++= ____________________ 2. 2460xx−+= ______________________
3. 2
35xx+= ________________________ 4. 2750xx−+= ______________________
5. 2340xx−+= _____________________ 6. 2
52
x
x−= _________________________
7. 2
3730xx−+= ____________________ 8. 2390xx−+= ______________________
9. 2
21
4
x
x
+=
_______________________ 10. 2
2340xx−+= _____________________
11. 2220xx−−= ____________________ 12. 2
56
x
x=− _________________________
Extra Practice Exercises 749
EXTRA PRACTICE 30 (continued)
Solving Quadratic Equations Using the Quadratic Formula
Use after Section 11.2
13. 2
13
50
xx
−+ = _____________________ 14. 26120xx−+= _____________________
15. 236xx−= ________________________ 16. 2
854
x
x−=− _______________________
17. 2
25
30
xx
++ = _____________________ 18. 212 10
x
x+= _______________________
19. 246
x
x+= _______________________ 20. 2
610xx−−= ______________________
21. 2
10 4 1 0xx−−= ___________________ 22. 2
22
7
x
x
−= _________________________
23. 2520xx−+= ____________________ 24. 2
3810xx+= _______________________
25. 2
432xx=+ ______________________ 26. 2950xx++= ______________________
27. 2830xx−+= _____________________ 28. 2
282xx=+ _______________________
29. 2
7230xx−+= ____________________ 30. 2
15 2 10 0xx−−= ___________________
750 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 31
Solving Problems Using Quadratic Equations
Use after Sections 11.1 and 11.4 Name ____________________________
Example: $3600 was invested at interest rate ,r compounded annually. In 2 years, it grew to
$3969. What was the interest rate?
We use the compound-interest formula,
()
1,
t
AP r=+ to solve this problem.
$3969, $3600, 2,APt=== and we solve for .r
()
()
()
2
2
1
3969 3600 1
3969
1
3600
3969
1
3600
63
1
60
60 63
63 60
3 1 123 41
60 20 60 20
t
AP r
r
r
r
r
r
ror r
=+
=+
=+
±=+
±=+
−±=
== − =−=
Since the interest rate cannot be negative, we need only check 1,
20 or 5%. 5% does check, so the interest
rate was 5%.
Solve. Use a calculator and approximate answers to the nearest tenth of a percent or tenth of a second.
1. $2000 was invested at interest rate r, compounded annually. In 2 years, it grew to $2333.
What was the interest rate? ________________
2. The formula
s
=16t2 is used to approximate the distance s, in feet, that an object falls freely from
rest in t seconds. Use the formula to find how long it would take an object to fall freely from the top
of the 984 ft tall Eiffel Tower. ________________
3. $5500 was invested at interest rate r, compounded annually. In 2 years, it grew to $6180. What was
the interest rate? ________________
4. Use the formula
s
=16t2to find the approximate time t, that an object falls freely from rest from a
height of 1325 ft. ________________
5. $7000 was invested at interest rate r, compounded annually. In 2 years, it grew to $7836. What was
Extra Practice Exercises 751
EXTRA PRACTICE 31 (continued)
Solving Problems Using Quadratic Equations
Use after Sections 11.1 and 11.4
See Section 11.4 for examples of problem solving involving work and motion problems.
6. A boat travels 40 miles upstream and then turns around and travels 40 miles downstream. The total
time for both trips is 6 hours. If the stream flows at 5 mph, how fast does the boat travel in still
water? ________________
7. It takes Jim 15 hours longer to build a wall than it does Corey. If they work together, they can build
the wall in 18 hours. How long would it take Corey to build the wall alone? ________________
8. Jose’s motorcycle traveled 270 mi at a certain speed. Had he gone 15 mph faster, the trip would have
taken 3 hr less. Find the speed of the motorcycle. ________________
9. Gary and Marsha work together to type a short story, and it takes them 6 hr. It would take Marsha
5 hr more than Gary to type the story alone. How long would each need to type the story if they
worked alone? ________________
10. Karen’s Honda travels 432 mi at a certain speed. If the car had gone 6 mph slower, the trip would
have taken 1 hr more. Find Karen’s speed. ________________
11. It takes Danielle 2 hours longer to deliver the papers than it does Stan. If they work together it takes
them 1 hour. How long would it take Danielle to deliver the papers alone? Round the answer to the
nearest tenth of an hour. ________________
12. A boat travels 16 miles upstream and then turns around and travels 16 miles downstream. The total
time for both trips is 4 hours. If the stream flows at 2 mph, how fast does the boat travel in still
water? Round the answer to the nearest tenth. ________________
752 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 32
Solving Equations Reducible to Quadratic
Use after Section 11.5 Name ____________________________
Example: Solve
()()
2
13 1113 28 0xx+−++=
Let 13ux=+ and substitute u for 13
x
+.
()()
2
11 28 0
74 0
uu
uu
−+=
−−=
7 0 4 0uoru−= −=
7 4uoru==
Substitute 13
x
+ for u and solve for
x
.
13 7 13 4
3 6 3 3
2 1
4 1
xor x
xor x
xor x
x
or x
+= +=
==
==
==
Both values check. The solutions are 4 and 1.
Solve.
1. 6270aa−−=
___________________ 2. 42
8120xx−+= ____________________
3. 21
55600xx
−−
−−= _________________ 4.
()()
2
31 231150xx−+ −−= ___________
5. 10 9 0aa−+=
_____________________ 6.
()()
2
555240xx−+−−= _____________
Extra Practice Exercises 753
EXTRA PRACTICE 32 (continued)
Solving Equations Reducible to Quadratic
Use after Section 11.5
7. 42
680xx−+= _______________________ 8. 13 36 0xx−+= ______________________
9.
()()
2
22
211 2240yy yy−− −+= 10.
42
4210xx+−= _______________________
__________________
11.
()()
2
22
525240xx xx−− −−= 12. 12 20 0aa−+= ______________________
__________________
13.
()()
2
42 1042250xx+− ++=
14.
()()
2
713 7400xx−− −+=
__________________ ____________________
15. 42
7120xx−+= _____________________ 16. 21
27150yy
−−
+−=_____________________
754 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 33
Graphing Quadratic Functions
Use after Sections 11.6 and 11.7 Name ____________________________
Example: Graph:
()
243fx x x=− + − .
()
()
()
()
2
2
2
2
() 4 3
4 4 4 3
4 4 4 3
2 1
fx x x
xx
xx
x
=− − −
ªº
=− − + − −
¬¼
=− − + + −
=− − +
Line of symmetry: 2x=
Vertex:
()
2, 1
x
()
f
x
2
1
3
0
4
1
0
0
í3
í3
y
x
–5 –2 –1–1
1
2
3
4
5
(2, 1)
x = 2
f(x) = –x
2
+ 4x–3
–2
–3
–5
–3–4
–4
12345
Graph.
1.
()
2
3
f
xx= 2.
() ( )
2
1fx x=− 3.
() ( )
2
23fx x=− +
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
4.
() ( )
2
231fx x=−+ 5.
()
267fx x x=−+ 6.
()
2
4
f
xx=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 755
EXTRA PRACTICE 33 (continued)
Graphing Quadratic Functions
Use after Sections 11.6 and 11.7
7.
()
242fx x x=++ 8.
() ( )
2
31fx x=− 9.
()
2
22047fx x x=− − −
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
10.
() ( )
2
3fx x=+ 11.
()
2
1
2
f
xx=− 12.
() ( )
2
12fx x=− −
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
13.
()
2
21629fx x x=−+ 14.
() ( )
2
21fx x=− 15.
()
269fx x x=++
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
756 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 33 (continued)
Graphing Quadratic Functions
Use after Sections 11.6 and 11.7
16.
()
2
1.5
f
xx= 17.
() ( )
2
234fx x=− + + 18.
()
223
f
xx x=−+
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
19.
() ( )
2
1fx x=+ 20.
() ( )
2
23fx x=+ − 21.
()
2
42435fx x x=− + −
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
22.
() ()
2
114
2
fx x=− + + 23.
() ( )
2
21fx x=− − 24.
()
2
4
f
xx=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
Extra Practice Exercises 757
EXTRA PRACTICE 33 (continued)
Graphing Quadratic Functions
Use after Sections 11.6 and 11.7
25.
()
267fx x x=++ 26.
() ( )
2
4fx x=− + 27.
()
2
441
f
xxx=−+
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
28.
() ()
2
13
3
fx x=+ 29.
()
249fx x x=− − − 30.
()
2
243
f
xxx=−−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
31.
() ( )
2
21fx x=+ − 32.
() ( )
2
411fx x=− − + 33.
() ()
2
14
4
fx x=−
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
y
x
–5 –2 –1–1
1
2
3
4
5
–2
–3
–5
–3–4
–4
12345
758 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 34
Polynomial Inequalities and Rational Inequalities
Use after Section 11.9 Name ____________________________
See Section 11.9 for Examples.
Solve.
1.
()( )
6100xx−+< __________________ 2.
()()
830xx−+>____________________
3.
()()
520xx+−≥ __________________ 4.
()()
370xx−+≤ ___________________
5. 212 0xx+− > _____________________ 6. 220 0xx−− > ______________________
7. 260xx−−≤ ______________________ 8. 23540xx+−< _____________________
9.
()( )( )
1690xx x++ −> _____________ 10.
()()( )
57100xxx−+−< _____________
11.
()()()
5230xxx+−+≤ _____________ 12.
()()( )
26110xxx+−+> _____________
13 .
()()()
6380xxx−+−> _____________ 14.
()( )()
71210xx x−+ +≥ _____________
15.
()()()
10 4 4 0xxx−+−≤ ____________ 16.
()()()
8980xxx++−> ______________
Extra Practice Exercises 759
EXTRA PRACTICE 34 (continued)
Polynomial Inequalities and Rational Inequalities
Use after Section 11.9
Solve.
17. 40
8
x
>
− _________________________ 18. 20
3
x
<
+ __________________________
19. 0
6
x
x
≥
+ _________________________ 20. 10
9
x
x
+≤
− __________________________
21. 40
5
x
x
−<
+ _________________________ 22. 60
1
x
x
−>
+ __________________________
23. 30
8
x
x
+<
− _________________________ 24. 70
4
x
x
+<
− __________________________
25. 21
0
4
x
x
+≥
+ ________________________ 26. 40
3
x
x
−>
− __________________________
27. 32
0
4
x
x
+<
− ________________________ 28. 20
1
x
x
+>
+ __________________________
29.
()( )
12
0
xx
++
>
()()
34
0
xx
+−
≥
760 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 35
Solving Exponential Equations and Logarithmic Equations
Use after Section 12.6 Name ____________________________
Examples. Solve.
a) 1
13
7 343
77
13
4
x
x
x
x
−
−
=
=
−=
=
b) 6 15
log 6 log15
log 6 log15
log15
log 6
1.5114
x
x
x
x
x
=
=
=
=
≈
c)
3
3
0.04
ln ln 0.04
3ln ln0.04
3 ln 0.04
ln 0.04
3
1.0730
t
t
e
e
te
t
t
t
−
−
=
=
−=
−=
=−
≈
Solve. Where appropriate, round to 4 decimal places.
1. 5
381
x= __________________________ 2. 4120
t
e= __________________________
3. 4 6
x= ___________________________ 4. 6 2
x= ____________________________
5. 20.6
t
e−= _________________________ 6. 32
5625
x+= _________________________
7. 1
816
x+= __________________________ 8. 10 7
x= ____________________________
9. 7 1520
x= ________________________ 10. 0.04 10
t
e= __________________________
11. 55
t
e= ___________________________ 12. 6 7.1
x= ___________________________
13. 3
636
x+= _________________________ 14. 1
43
x−= ___________________________
15. 23
12 16
x−= ________________________ 16. 5
10 1000
x−= _______________________
Extra Practice Exercises 761
EXTRA PRACTICE 35 (continued)
Solving Exponential Equations and Logarithmic Equations
Use after Section 12.6
Examples. Solve:
() ()
22
log 1 log 1 4xx+− −=
() ()
22
2
log 1 log 1 4
1
log 4
1
1
16
1
1 16 16
17 15
xx
x
x
x
x
xx
x
+− −=
+=
−
+=
−
+= −
=
17
15 x=
The solution is 17
15 .
Check:
() ()
22
22
22
2
2
log 1 log 1 = 4
______
17 17
log 1 log 1
15 15
32 2
log log
15 15
32 2
log 15 15
log 16
xx+− −
§· §·
+− −
¨¸ ¨¸
©¹ ©¹
−
§·
÷
¨¸
©¹
4
?
TRUE
4
Solve.
17.
()
log log 15 2xx++= 18.
()
log 2 log 3xx+− =
_________________________________ __________________________________
19.
()
3
log 2 7 4x−= 20.
()
5
log 11 2x−=
_________________________________ __________________________________
21.
()
log log 21 2xx+−= 22.
() ()
22
log 2 log 2 5xx−+ +=
_________________________________ __________________________________
23.
()
log 3 4 1x+= 24.
()
log 33 log 2xx+− =
_________________________________ __________________________________
25.
()
log log 5 1xx−+=− 26.
()
44
log 3 log 3xx+− =
_________________________________ __________________________________
27.
() ()
44
log 6 log 6 3xx−+ += 28.
()
66
log log 9 2xx+−=
_________________________________ __________________________________
29.
()
log log 0.21 2xx+−=− 30.
()
log 48 log 2xx−+ =
_________________________________ __________________________________
31.
()
77
log log 4 21 3xx++= 32.
()
2
log 5 4x−=
_________________________________ __________________________________
762 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 36
Solving Nonlinear Systems of Equations
Use after Section 13.4 Name ____________________________
Example. Solve:
22
22
4163,
27.
yx
xy
=−
=+
22 22
22 2 2
2
2
3416 3416
2 7 8 4 28 (Multiplying by 4)
11 44 (Adding)
4
xy xy
xy x y
x
x
+=→ +=
−= → − =
=
=
2
x=±
If 2,x= 24,x= and if 2,x=− 24x= so substituting 2 or í2 in 22
27,xy=+ we have
2
2
24 7
1
1
y
y
y
⋅= +
=
±=
The solutions are
()
2, 1 ,
()
2, 1−,
()
2, 1−, and
()
2, 1−−.
Solve.
1. 22
20,
8
xy
xy
+=
=
4.
22
82,
9
xy
xy
+=
=−
7. 22
25 100,
10 2 20
xy
xy
+=
+=
10. 22
34,
2
xy
yx
+=
−=
2. 22
22
49,
49
xy
xy
+=
−=
5. 22
416,
24
xy
yx
+=
=−
8.
22
22
36 ,
36
xy
xy
=−
=+
11.
2
22
8,
20
xy
xy
−=
+=
3.
22
25 ,
1
xy
yx
−=−
−=
6.
22
41,
54 0
xy
xy
+=
−=
9.
22
22
325,
325
yx
xy
−=
+=
12.
22
2
64,
8
xy
yx
+=
=+
Extra Practice Exercises 763
EXTRA PRACTICE 36 (continued)
Solving Nonlinear Systems of Equations
Use after Section 13.4
13. A rectangle has perimeter 170 cm, and the length of a diagonal is 65 cm. What are its dimensions?
________________
14. The area of a rectangle is 2
12 2 m . The length of a diagonal is 34 m. Find the dimensions.
________________
15. The product of two numbers is 44−. The sum of their squares is 137. Find the numbers.
________________
16. The sum of the squares of two positive numbers is 89. Their difference is 3. What are the numbers?
________________
17. The sum of the squares of two positive integers is 58. Their difference is 4. What are the integers?
________________
18. The perimeter of a rectangle is 44 m and the area is 105 m2. What are the dimensions of the
rectangle? ________________
19. The product of two numbers is 1
6. The sum of their squares is 13
36 . Find the numbers.
________________
20. The area of a rectangle is 0.48 cm2. The length of a diagonal is 1.0 cm. Find the dimensions of the
rectangle. ________________
764 Instructor Resource Manual Elementary and Intermediate Algebra: Concepts and Applications, Sixth Edition
EXTRA PRACTICE 37
The Binomial Theorem
Use after Sectiɨn 14.4 Name ____________________________
Examples:
a) 5! 54321 120=⋅⋅⋅⋅=
b)
()
77! 7 6 5 4 3 2 1 35
37 3!3! 4321321
§· ⋅⋅⋅⋅⋅⋅
== =
¨¸ −⋅⋅⋅⋅⋅⋅
©¹
c) Expand:
()
4
25.
x
y−
Using the binomial theorem
()
122
01 2
nnn n n
nn n n
ab a ab a b b
n
−−
§· §· §· §·
+= + + ++
¨¸ ¨¸ ¨¸ ¨¸
©¹ ©¹ ©¹ ©¹
“.
2, 5, 4axb yn==−=
() ()( ) ()( ) ()( ) ( )
()()
()
()( )
()
()()
43 22 3 4
43 22 3 4
43 22 3 4
44 4 4 4
2252525 5
01 2 3 4
1 16 4 8 5 6 4 25 4 2 125 1 625
16 160 600 1000 625
x
xy xy xy y
xxyxyxy y
xxyxy xy y
§· §· §· §· §·
=+ −+ −+−+−
¨¸ ¨¸ ¨¸ ¨¸ ¨¸
©¹ ©¹ ©¹ ©¹ ©¹
=+−+ +−+
=− + − +
Simplify.
1. 7! _______________________________ 2. 9! ________________________________
3. 8! ______________________________ 4. 5!
3! _______________________________
5. 4
3
§·
¨¸
©¹
_____________________________ 6. 9
6
§·
¨¸
©¹
______________________________
7. 12
8
§·
¨¸
©¹
____________________________ 8. 25
25
§·
¨¸
©¹
_____________________________
9. 12
2
§·
¨¸
©¹
____________________________ 10. 18
1
§·
¨¸
©¹
_____________________________
Extra Practice Exercises 765
EXTRA PRACTICE 37 (continued)
The Binomial Theorem
Use after Sectiɨn 14.4
Expand each of the following.
11.
()
5
x
y+ __________________________ 12.
()
6
x
y− ___________________________
13.
()
3
2
x
y+ _________________________ 14.
()
3
32
x
y− _________________________
15.
()
5
3
x
y− _________________________ 16.
()
6
2
x
y+ __________________________
17.
()
8
x
y+ __________________________ 18.
()
4
32
x
y− _________________________
19.
()
3
x
y−+ _________________________ 20.
()
5
2
x
y− __________________________
21.
5
1
xy
§·
+
¨¸
©¹
_________________________ 22.
3
5
2xy
§·
−
¨¸
©¹
_________________________
Find the indicated term of the binomial expansion.
23.
()
7
5th,
x
y+ ______________________ 24.
()
9
6th, 2 3
x
y− _____________________
25.
()
10
2
8th, 2 3xy+ ___________________ 26.
()
8
7th, 3 2
x
y+ _____________________