Chapter 9 Summary and Review: Study Guide 253
Find the vertices as follows:
44. 4(3x+4)=2−x
13
46. 10x−8(3x−7) = 2(4x−1)
48. 0.5x−2.34+2.4x=7.8x−9
2.9x−2.34=7.8x−9
54. f(2a)=|2−2a|,or2|1−a|
Chapter 9 Vocabulary Reinforcement
bers that are common to A and B.
5. When two or more sentences are joined by the word and
8. The union of two sets A and B is the collection of elements
11. A quantity is at least some amount q:x≥q.
Chapter 9 Concept Reinforcement
3. False; see page 630 in the text.
Chapter 9 Study Guide
1. 8−3x≤3x+6
−2 : We substitute and get 8 −3(−2) ≤3(−2) + 6,
or 8 + 6 ≤−6+6, or 14 ≤0, a false sentence.
Therefore, −2 is not a solution.
2. a) Interval notation for {t|t<−8}is (−∞,−8).
3. 5y+5<2y−1
3y+5<−1
y
254 Chapter 9: More on Inequalities
4. −4≤5x+6<11
5. z+4<3or 4z+1≥5
z<−1or 4z≥4
6. |5x−1|=9
5x−1=−9or 5x−1=9
7. |z+4|=|3z−2|
z+4=3z−2or z +4=−(3z−2)
−2z+4=−2or z +4=−3z+2
8. a) |2x+3|<5
b) |3x+2|≥8
3x+2≤−8or 3x+2≥8
9. Graph: 3x−2y>6
which half-plane to shade, test a point not on the line. We
contain (0,0).
10. Graph: x−2y≤4,(1)
lap.
To find the vertices we solve three different systems of
equations. From (1) and (2) we obtain the vertex (4,0).
Chapter 9 Review Exercises
⫺
660
⫺
5
⫺
4
⫺
3
⫺
2
⫺
154321
Chapter 9 Summary and Review: Review Exercises 255
4. x−2≤−4
7. y−5≥−12
8. 4y>−16
9. −0.3y<9
10. −6x−5<13
11. 4y+3≤−6y−9
12. −1
2x−1
4>1
2−1
4x
13. 0.3y−8<2.6y+15
14. −2(x−5) ≥6(x+7)−12
15. Familiarize. Let t= the length of time of the move, in
hours. Then Metro Movers charges 85+40tand Champion
20t>85
Check. When t=17
4hr, Champion Moving charges
4= 85 + 170 = $255. For a value of tgreater
State. Champion Moving is more expensive for moves tak-
Translate.
Interest on
is at
−0.01x+ 1200 ≥1100
256 Chapter 9: More on Inequalities
21. 2x−5<−7and 3x+8≥14
23. −15 <−4x−5<0
2>x>−5
4Dividing by −4 and reversing
the inequality symbol
5
2x<−22 or −4x≤24
x<−11 or x ≥−6
−3
30. |−23 −39|=|−62|= 62, or
32. |x−2|=7
33. |2x+5|=|x−9|
3.
34. |5x+6|=−8
35. |2x+5|<12
−12 <2x+5<12
37. |3x−4|≥15
38. |x|<0
y
y
x
Chapter 9 Summary and Review: Review Exercises 257
39. Graph: 2x+3y<12
First graph the line 2x+3y= 12. Draw it dashed since the
(0,0) and draw the graph.
40. Graph: y≤0
First graph the line y= 0 (the x-axis). Draw it solid
41. Graph: x+y≥1
0FALSE
42. Graph: y≥−3,
x≥2
43. Graph: x+3y≥−1,
44. Graph: x−y≤3,(1)
y
x
(5, 2)
(⫺3, 2)
⫺660⫺5⫺4⫺3⫺2⫺154321
258 Chapter 9: More on Inequalities
45. −2(x+3)−1<−2(2 −x)
The solution set is −3
4,∞. Answer D is correct.
46. −1
3x−10≥30
47. |2x+5|≤|x+3|
|2x+5|≤x+3 or |2x+5|≤−(x+3)
First we solve |2x+5|≤x+3.
Chapter 9 Discussion and Writing Exercises
2. The distance between xand −5 is |x−(−5)|,or|x+5|.
4. The solutions of |x|≥6 are those numbers whose dis-
Chapter 9 Test
1. Interval notation for {x|−3<x≤2}is (−3,2].
4. −4y−3≥5
−4y≥8
Chapter 9 Test 259
8. −5y−1>−9y+3
9. 4(5 −x)<2x+5
x> 5
10. −8(2x+3)+6(4−5x)≥2(1 −7x)−4(4+6x)
11. Familiarize. Let t= the length of time of the move,
in hours. Then Motivated Movers charges 105 + 30tand
Quick-Pak Moving charges 80t.
Quick-Pak
than
Motivated Movers
Check. When t=21
10 hr, Motivated Movers charges
105 + 30 ·21
12. Familiarize. We will use the formula P=1+ d
33.
Translate. We want to find those values of Pfor which
2≤1+ d
33 ≤d≤231
14. Interval notation for x<−3or x > 4is(−∞,−3)∪(4,∞).
The intersection of {x|x≥2}and {x|x≥4},is{x|x≥4},
or [4,∞).
16. −3<x−2<4
17. −11 ≤−5x−2<0
18. −3x>12 or 4x>−10
x<−4or x > −5
numbers, or (−∞,∞).
20. 3x−2<7or x −2>4
y
x
260 Chapter 9: More on Inequalities
7
26. |x|=9
27. |x−3|=9
28. |x+10|=|x−12|
x+10=x−12 or x +10 = −(x−12)
29. |2−5x|=−10
30. |4x−1|<4.5
31. |x|>3
32.
6−x
33. |−5x−3|≥10
34. Graph: x−6y<−6
We first graph the line x−6y= 6. We draw the line dashed
x−6y<−6
0−6·0?−6
Graph the lines x+y= 3 and x−y= 5 using solid lines.
x+y=3,
x−y=5
y
y
37.
1
2x−2≥2.2
38. |3x−4|≤−3
39. 7x<8−3x<6+7x
7x<8−3x and 8−3x<6+7x
The intersection of xx< 4
Cumulative Review Chapters 1 – 9
1. Graph y=−5x+4.
2. Graph 3x−18 = 0.
3. Graph x+3y<4.
First we graph the equation x+3y= 4. We use a dashed
(0,0).
4. x+y≥4,
region for each inequality and shade the region where they
overlap.
262 Chapter 9: More on Inequalities
x+y=4,
5. g(x)=|x−4|+5
7. From the graph we see that the inputs extend from −5 to
11. 9x2−25
x2−16 ÷3x+5
x−4=9x2−25
x2−16 ·x−4
3x+5
12. 2x+1
4x−12 −x−2
5x−15
13. 1−2
y2
1−2
y2
=
y2·y3
1·y3−1
y3·y3
=2
x+2+3
x−2−x+1
(x+ 2)(x−2)
−422−46
2−11 23 −49
9y−5y+3=33
4y+3=33
Cumulative Review Chapters 1 – 9 263
19. 3x
x−2−6
x+2 =24
x2−4
20. P=3a
a+b
21. F=9
5C+32
22. |x|≥2.1
23. 6
x−5=2
2x
6
4x−1=0 or 4x−1=0
Multiply Equation (1) by 3 and Equation (2) by −2 and
then add.
12x−6y=18
27. 4x+5y=−3,(1)
x=1−3y(2)
The solution is (−2,1).
28. x+2y−2z=9,(1)
264 Chapter 9: More on Inequalities
Now solve the system of Equations (4) and (5). We mul-
tiply Equation (5) by 2 and then add.
4x+4y+z=2,(2)
3x+2y−4z= 5 (3)
3x+2y−4z=5
−76x−72y=−52
Substitute 1
16 for yin Equation (4) and solve for x.
Finally, substitute 5
8for xand 1
16 for yin Equation (2)
x2+8x−84 = (x+ 14)(x−6)
33. 6x2+11x−10
Using trial and error or the ac-method, we have
37. 0.027b3−0.008c3=(0.3b)3−(0.2c)3=
39. 20x2+7x−3
40. We will use the point-slope equation.
y−y1=m(x−x1)
41. First we find the slope of the given line.
42. Familiarize. Let x,y, and zrepresent the number of
wins, losses, and ties, respectively.
Losses are wins less 8.
↓↓↓↓↓
y=x−8
43. Let W= the amount of waste generated, in pounds, and
238 = k·2000
44. x
x−4−4
x+3=28
x2−x−12
45. x2−x−6=6
46. Familiarize. Let t= the number of hours it would take
the ships to fill the tank, working together.
6
10 +6
15 =18
30 +12
30 =30
30 =1
47. We substitute for xand y, using the three given points.
48. 16x3=x
16x3−x=0
x(16x2−1) =
49. 18
x−9+10
x+5=28x
x2−4x−45
18
x−9+10
x+5=28x
(x−9)(x+5)