Chapter 2
Solving Equations and Inequalities
Exercise Set 2.1
6. 8y=−72
8. y
8=6
10. 9x+5=86
12. 6(y−2) = 18
−5 is not a solution.
14. 7
26. 4
28. 25
40. y−3
4=5
6
12
42. −1
46. 16
53
52. 1363
8
18 Chapter 2: Solving Equations and Inequalities
62. x+4=5+x
Exercise Set 2.2
6. 7
16. 8
26. −x
30. 2
5y=−4
15
x=120
42. −x
48. −32y
50. 2−5(x+5)=2−5x−25 = −5x−23
62. a2+1
c
Exercise Set 2.3
RC2. The correct answer is (a).
4. 4y+10=46
4y=36
12. −91=9t+8
−99=9t
−11 = t
24. −5y−7y= 144
−12y= 144
4x=10
x=4
5·10
x=8
−3=x
34. 5y−2=28−y
−8z−7=17
−8z=24
z=−3
50. 1
52. 1−2
56. 1.7t+8−1.62t=0.4t−0.32+8
58. 5
16y+3
8y=2+1
4y, LCM is 16
60. 8(3x+2)=30
62. 9 = 3(5x−2)
66. y−2
72. 10 −3(2x−1)=1
74. 3(t−2) = 9(t+2)
The equation has no solution.
84. 13 −(2c+2)=2(c+2)+3c
1=c
86. 5[3(7 −t)−4(8+2t)] −20 = −6[2(6 + 3t)−4]
19 =t
88. 6(2x−1) −12 = 7 + 12(x−1)
Exercise Set 2.4 21
92. 0.9(2x+8)=20−(x+5)
14
94. −75.14
100. 256 ÷64 ÷42= 256 ÷64 ÷16
102. 1
104. 5(3x+2)=75
Exercise Set 2.4
RC4. z=w+4
2. B=30·1800 = 54,000 Btu’s
20. y−A=x
24. y=q−x
26. y=−x
W+b=mt
b=x
34. d=rt
38. A=1
h=b
22 Chapter 2: Solving Equations and Inequalities
44. Q=p−q
46. I=Prt
P
3
x=−1
62. 5a= 3(6 −3a)
4+7n=m
66. Not necessarily; 6 = 2 ·2+2·1,but 2 ·6,or 12, can be
Chapter 2 Mid-Chapter Review
2. True; see page 85 in the text.
4. False; see page 102 in the text.
7. 5y+z=t
5
8. x+5=11
9. x+9=−3
x+9−9=−3−9
11. −7=y+3
13. y−7=−2
y−7+7=−2+7
Chapter 2 Mid-Chapter Review 23
14. −3
The solution is 3
4.
15. −3.3=−1.9+t
16. 7x=42
17. 17 = −t
19. −5y=−85
−5y
−5=−85
−5
20. x
The solution is 21.
21. 2
22. −t
5=3
23. 3
4x=−9
8
x=−3
3x+2−2=5−2
The solution is −3.
26. 6x−7=2
6=9
6
27. −4x−9=−5
−4x−9+9=−5+9
24 Chapter 2: Solving Equations and Inequalities
28. 6x+5x=33
29. −3y−4y=49
30. 3x−4=12−x
31. 5−6x=9−8x
5−6x+8x=9−8x+8x
2x
32. 4y−3
2=3
4+2y
3
8.
33. 4
24 + 5t−24=3−24
The solution is −21
5.
34. 0.21n−1.05 = 2.1−0.14n
35n= 315
35n
35. 5(3y−1) = −35
15 =−30
15
y=−2
37. −8+t=t−8
Exercise Set 2.5 25
38. z+12=−12 + z
41. A=4b
A
43. n=s−m
n−s=s−m−s
4t
46. M=x+y+z
Exercise Set 2.5
p=0.25 = 25%
4. Solve: 20.4 = 24% ·a
85 = a
19% = p
10. Solve: 7 = 175% ·b
26 Chapter 2: Solving Equations and Inequalities
20. Any number is 100% of itself, so 70 is 100% of 70. We
24. Solve: a= 40% ·2
a=0.8
36. Solve: a=54.8% ·$2360
a≈$1293 million
42. a) Solve: a= 20% ·$75
44. a) Solve: $6.75 = 18% ·b
$37.50 = b
50. Decrease: 301 −273 = 28
54. Decrease: 4381 −962 = 3419
56. 5x−21
58. −18b
12b=−3·6/ ·b/
2·6/ ·b/−3
2
62. Note: 4 ft 8 in. = 56 in.
Exercise Set 2.6
4. Solve: x+(x+2)=72
6. Solve: 3a+72,000 = 876,000
10. Solve: x+(x+ 1) = 547
a=35
Whitney, Wesley, and Wanda’s ages are 35, 36, and 37,
x0
54321 123450
5 x2
Exercise Set 2.7 27
16. Solve: 2(w+2)+2w=10
p= $110
22. Solve: 84.45+0.55m= 250
30. Solve: b+0.1b= 7194
b= $6540
36. Solve: t+2t+27
38. Solve: 2x+85= 3
4x
44. −25.6÷(−16) = 1.6
54. Let d= the number of dimes. Then 2d= the number of
quarters, and d+ 10 = the number of nickels.
Exercise Set 2.7
6.
16. x+5>2
18. x+8≤−11
54321 123450
28 Chapter 2: Solving Equations and Inequalities
22. 2x+4>x+7
30. x−1
34. 8x≥32
x≥4
36. −16x>−64
38. 3x<−4
40. −3x≤15
x≥−5
42. −7x<−21
46. −4x≤1
50. 3+4y<35
4y<32
56. 48 >13 −7y
58. 15x+5−14x≤9
60. −8<9x+8−8x−3
−8<x+5
−13 <x
2>y
{y|y<2}
66. 18 −6y−4y<63+5y
Exercise Set 2.8 29
68. 0.96y−0.79 ≤0.21y+0.46
10+3x<4
3x<−6
76. 3(5+3m)−8≤88
15 + 9m−8≤88
80. 5(x+3)+9≤3(x−2)+6
5x+15+9≤3x−6+6
82. 0.4(2x+8)≥20 −(x+5)
84. 1−2
3y≥9
5−y
5+3
5
94. The solutions of |x|<3 are all points whose distance from
Exercise Set 2.8
30 Chapter 2: Solving Equations and Inequalities
10. T≤−2◦
The solution set is {s|s≥97}.
24. Solve: 9
5C+32>98.6
32. Solve: 0.45+0.25h≥2.20
36. Solve: 5+7+8+c
46. Solve: 1
2·8·h≤12
h≤3ft
48. Solve: 3 + 3
50. Solve: h+(h+3)>27
54. 8x+3x=66
11x=66
62. Solve: 4 + 2.5(h−1) >16.5
Chapter 2 Vocabulary Reinforcement
Chapter 2 Concept Reinforcement
1 0
Chapter 2 Summary and Review: Review Exercises 31
2. True; for any number n,n≥nis true because n=nis
4. True; if x>y, then −1·x<−1·y(reversing the inequality
Chapter 2 Study Guide
−2x=24
2. 4+3y−7= 3+3(y−2)
4. A=1
2bh
6. Graph: x≤−1
3y+5>−7
3y+5−5>−7−5
Chapter 2 Review Exercises
x=−22
The solution is −22.
5. −2
3x=−1
6
7. −x
4=48
9. 4
4·4
5y=5
4·−3
16
10. 5−x=13
11. 1
4x−5
8=3
8
12. 5t+9= 3t−1
2t
13. 7x−6=25x
−9=−27
−9
y=3
15. 0.22y−0.6=0.12y+3−0.8y
0.9y=3.6
16. 1
4x−1
8x=3−1
16x
2
16
3·3
16x=16
3·3
17. 14y+17+7y=9+21y+8