Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation. Graph and check your solutions.

9. | b | = 1 2 vertical line b vertical line equals , 1 half
10. 4 = | y |
11. | n | + 3 = 7
12. 7 = | s | − 3 7 equals vertical line s vertical line negative 3
13. | x | − 10 = − 2 vertical line x vertical line negative 10 equals negative 2
14. 5| d | = 20
15. − 3 | m | = − 9 negative 3 vertical line m vertical line equals negative 9
16. | y | + 3 = 3

See Problems 2 and 3.

Solve each equation. If there is no solution, write no solution.

17. | r − 8 | = 5 vertical line r minus 8 vertical line equals 5
18. | c + 4 | = 6
19. 2 = | g + 3 |
20. 3 = | m + 2 |
21. − 2 | 7 d | = 14 negative 2 vertical line 7 d vertical line equals 14
22. − 3 | 2 w | = − 12 negative 3 vertical line 2 w vertical line equals negative 12
23. 3 | v − 3 | = 9 3 vertical line v minus 3 vertical line equals 9
24. 2| d + 4 | = 8
25. | 4 f + 1 | − 2 = 5 vertical line 4 f plus 1 vertical line negative 2 equals 5
26. | 3 t − 2 | + 6 = 2 vertical line 3 t minus 2 vertical line plus 6 equals 2
27. 4 | 2 y − 3 | − 1 = 11 4 vertical line 2 y minus 3 vertical line negative 1 equals 11
28. 3| x + 2 | + 4 = 13
29. − 4 | k | = 12 negative 4 vertical line k vertical line equals 12
30. | − 3 n | − 2 = 4 vertical line negative 3 n vertical line negative 2 equals 4
31. − 4 | k + 1 | = 16 negative 4 vertical line k plus 1 vertical line equals 16

See Problems 4 and 5.

Solve and graph each inequality.

32. | x | ≥ 3 vertical line x vertical line greater than or equal to 3
33. | x | < 5 vertical line x vertical line less than 5
34. | x + 3 | < 5 vertical line x plus 3 vertical line less than 5
35. | y + 8 | ≥ 3 vertical line y plus 8 vertical line greater than or equal to 3
36. | y − 2 | ≤ 1 vertical line y minus 2 vertical line less than or equal to 1
37. | p − 7 | ≤ 3 vertical line p minus 7 vertical line less than or equal to 3
38. | 2 c − 5 | < 9 vertical line 2 c minus 5 vertical line less than 9
39. | 3 t + 1 | > 8 vertical line 3 t plus 1 vertical line greater than 8
40. | 4 w + 1 | > 11 vertical line 4 w plus 1 vertical line greater than 11
41. | 5 t − 4 | ≥ 16 vertical line 5 t minus 4 vertical line greater than or equal to 16
42. | 4 x + 7 | > 19 vertical line 4 x plus 7 vertical line greater than 19
43. | 2 v − 1 | ≤ 9 vertical line 2 v minus 1 vertical line less than or equal to 9
44. | 3 d − 7 | > 28 vertical line 3 d minus 7 vertical line greater than 28
45. | 2 f + 9 | ≤ 13 vertical line 2 f plus 9 vertical line less than or equal to 13
46. | 5 m − 9 | ≥ 24 vertical line 5 m minus 9 vertical line greater than or equal to 24
47. Quality Control The ideal length of one type of model airplane is 90 cm. The actual length may vary from ideal by at most 0.05 cm. What are the acceptable lengths for the model airplane?
48. Basketball The ideal circumference of a women's basketball is 28.75 in. The actual circumference may vary from the ideal by at most 0.25 in. What are the acceptable circumferences for a women's basketball?

B Apply

Solve each equation or inequality. If there is no solution, write no solution.

49. | 2 d | + 3 = 21 vertical line 2 d vertical line plus 3 equals 21
50. 1.2 | 5 p | = 3.6 1.2 vertical line 5 p vertical line equals 3.6
51. | d + 1 2 | + 3 4 = 0 absolute value of . d plus , 1 half , end absolute value , . plus , 3 fourths , equals 0
52. | f | − 2 3 = 5 6 absolute value of f , , minus , 2 thirds , equals , 5 sixths
53. 3 | 5 y − 7 | − 6 = 24 3 vertical line 5 y minus 7 vertical line negative 6 equals 24
54. | t | + 2.7 = 4.5 vertical line t vertical line plus 2.7 equals 4.5
55. − 2 | c − 4 | = − 8.4 negative 2 vertical line c minus 4 vertical line equals negative 8.4
56. | y | − 3 = 5 fraction absolute value of y , , over negative 3 end fraction . equals 5
57. | n | − 5 4 < 5 vertical line n vertical line negative , 5 fourths , less than 5
58. 7 8 < | c + 7 | 7 eighths , less than vertical line c plus 7 vertical line
59. 4 − 3 | m + 2 | > − 14 4 minus 3 vertical line m plus 2 vertical line greater than negative 14
60. | − 3 d | ≥ 6.3 vertical line negative 3 d vertical line greater than or equal to 6.3
61. Think About a Plan The monthly average temperature T for San Francisco, California, is usually within 7.5°F of 56.5°F, inclusive. What is the monthly average temperature in San Francisco?
    • Should you model this situation with an equation or an inequality?
    • How can you use the given information to write the equation or inequality?

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