EXERCISES
For more practice, see Extra Practice.
Practice
Practiceand
andProblem
ProblemSolving
Solving
A
Practice by Example
Example 1
(page 167)
Example 2
(page 168)
Example 3
(page 169)
Solve each equation. If there is no solution, write no solution.
1. ∆b∆ = 2
2. 4 = ∆y∆
4. ∆n∆ + 2 = 8
5. 7 = ∆s∆ + 4
3. ∆w∆ = 12
6. ∆x∆ - 10 = -3
7. 4∆d∆ = 20
8. -3∆m∆ = -6
9. ∆y∆ + 3 = 3
10. 12 = -4∆k∆
11. 2∆z∆ - 5 = 1
12. 16 = 5∆p∆ - 4
Solve each equation. If there is no solution, write no solution.
13. ∆r - 8∆ = 5
14. ∆c + 2∆ = 6
15. 2 = ∆g + 1∆
16. 3 = ∆m + 2∆
17. ∆v - 2∆ = 7
18. -3∆y - 3∆ = 9
19. 2∆d + 3∆ = 8
20. -2∆7d∆ = -14
21. 1.2∆5p∆ = 3.6
22. Complete each statement with less than or greater than.
a. For ∆x∆ , 5, the graph includes all points whose distance is 9 5 units
from 0.
b. For ∆x∆ . 5, the graph includes all points whose distance is 9 5 units
from 0.
Solve each inequality. Graph your solution.
Example 4
(page 169)
23. ∆ k∆ . 2.5
24. ∆w∆ , 2
25. ∆x + 3∆ , 5
26. ∆n + 8∆ $ 3
27. ∆y - 2∆ # 1
28. ∆p - 4∆ # 3
29. ∆2c - 5∆ , 9
30. ∆2y - 3∆ $ 7
31. ∆3t + 1∆ . 8
32. ∆4x + 1∆ . 11
33. ∆5t - 4∆ $ 16
34. ∆3 - r∆ , 5
35. Manufacturing The ideal diameter of a gear for a certain type of clock is
12.24 mm. An actual diameter can vary by 0.06 mm. Find the range of
acceptable diameters.
36. Manufacturing The ideal width of a certain conveyor belt for a manufacturing
7
plant is 50 in. An actual conveyor belt can vary from the ideal by at most 32
in.
Find the acceptable widths for this conveyor belt.
B
Apply Your Skills
Solve each equation or inequality.
37. ∆2d∆ + 3 = 21
38. ∆–3n∆ - 2 = 7
40. ∆t∆ + 2.7 = 4.5
41. 4∆k + 1∆ = 16
39. ∆p∆ - 32 = 65
42. -2∆c - 4∆= -8
43. ∆3d∆ $ 6
44. ∆n∆ - 3 . 7
45. 9 , ∆c + 7∆
v | = -4.2
46. |23
47. ∆6.5x∆ , 39 48.
49. 12 a + 1 = 5
50. ∆a∆ + 21 = 3 12
u u
4∆n∆ = 32
51. 4 - 3∆m + 2∆ . -14
Write an absolute value inequality that represents each situation.
52. all numbers less than 3 units from 0
53. all numbers greater than 7.5 units from 0
54. all numbers more than 2 units from 6
55. all numbers at least 3 units from –1
Lesson 3-6 Absolute Value Equations and Inequalities
169-172
56. Manufacturing A pasta manufacturer makes 16-ounce boxes of macaroni.
The manufacturer knows that not every box weighs exactly 16 ounces. The
allowable difference is 0.05 ounce. Write and solve an absolute value inequality
that represents this situation.
Need Help?
10 4 2 means
10 + 2 or 10 - 2.
57. Elections In a poll for the upcoming mayoral election, 42% of likely voters
said they planned to vote for Lucy Jones. This poll has a margin of error of
4 3 percentage points. Use the inequality ∆v - 42∆ # 3 to find the least and
greatest percent of voters v likely to vote for Lucy Jones according to this poll.
58. Quality Control A box of one brand of crackers should weigh 454 g. The
quality-control inspector randomly selects boxes to weigh. The inspector
sends back any box that is not within 5 g of the ideal weight.
a. Write an absolute value inequality for this situation.
b. What is the range of allowable weights for a box of crackers?
59. Gears Acceptable diameters for one type of gear are from 6.25 mm to
6.29 mm. Write an absolute value inequality for the acceptable diameters
for the gear.
60. Writing Explain why the absolute value inequality ∆2c - 5∆ + 9 , 4
has no solution.
61. Open-Ended Write an absolute value equation using the numbers 5, 3, -12.
Then solve your equation.
Write an absolute value equation that has the given values as solutions.
Sample 8, 2
∆x - 5∆ = 3 Since 8 and 2 are both 3 units from 5, write »x – 5» ≠ 3.
62. 2, 6
63. -2, 6
64. -3, 9
65. 9, 16
66. –1, 7
67. 3, 8
68. –15, –3
69. 2, 10
70. Banking The ideal weight of a nickel is 0.176 ounce. To check that there are
40 nickels in a roll, a bank weighs the roll and allows for an error of 0.015
ounce in the total weight.
a. What is the range of acceptable weights if the wrapper weighs 0.05 ounce?
b. Critical Thinking For any given roll of nickels, can you be certain that all the
coins are acceptable? Explain.
71. a. Meteorology A meteorologist reported that the previous day’s temperatures
varied 14 degrees from the normal temperature of 258F. What were the
maximum and minimum temperatures possible on the previous day?
b. Write an absolute value equation for the temperature.
C
Challenge
Solve each equation. Check your solution.
72. ∆x + 4∆ = 3x
74. 43 ∆2x + 3∆ = 4x
73. ∆4x - 5∆ = 2x + 1
Replace the ■ with K, L, or ≠.
75. ∆a + b∆ ■ ∆a∆ + ∆b∆
76. ∆a - b∆ ■ ∆a∆ - ∆b∆
77. ∆ab∆ ■ ∆a∆?∆b∆
Za Z
78. P ba P ■ Z b Z , b 2 0
˛
˛
˛
˛
˛
Write an absolute value inequality that each graph could represent.
79.
169-172
⫺6 ⫺4 ⫺2
Chapter 3 Solving Inequalities
0
2
4
6
80.
⫺6 ⫺4 ⫺2
0
2
4
6
Standardized
Standardized
Test Prep Test Prep
Multiple Choice
81. Which compound inequality has the same meaning as ∆x + 4∆ , 8?
B. -12 . x . 4
A. -12 , x , 4
D. x . -12 or x , 4
C. x , -12 or x . 4
82. Which of the following values is a solution of ∆2 - x∆ , 4?
F. -2
G. -1
H. 6
I. 7
83. The ideal diameter of a metal rod for a lamp is 1.25 inches with an allowable
error of at most 0.005 inch. Which rod below would not be suitable?
A. a rod with diameter 1.249 inches
B. a rod with diameter 1.251 inches
C. a rod with diameter 1.253 inches
D. a rod with diameter 1.355 inches
84. A delivery driver receives a bonus if he delivers pizza to a customer in
30 minutes plus or minus 5 minutes. Which inequality or equation
represents the driver’s allotted time to receive a bonus?
F. ∆x - 30∆ , 5
G. ∆x - 30∆ . 5
H. ∆x - 30∆ = 5
I. ∆x - 30∆ # 5
85. Water is in a liquid state if its temperature t, in degrees Fahrenheit,
satisfies the inequality ∆t - 122∆ , 90. Which graph represents the
temperatures described by this inequality?
A.
32
B.
212
32
212
C.
Short Response
D.
90 122
90 122
86. A bicycling club is planning a trip. The graphs below show the number of
miles three people want to cycle per day.
Ramon
Kathleen
Allan
Take It to the NET
Online lesson quiz at
www.PHSchool.com
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
5
10
15
20
25
30
35
40
a. Draw a graph showing a trip length that would be acceptable to all
three bikers.
b. Explain how your graph relates to the graphs above.
Web Code: aea-0306
Lesson 3-6 Absolute Value Equations and Inequalities
169-172
Mixed Review
Lesson 3-5
Write a compound inequality to model each situation.
87. Elevation in North America is between the highest elevation of 20,320 ft above
sea level at Mount McKinley, Alaska, and the lowest elevation of 282 ft below
sea level at Death Valley, California.
88. Normal body temperature t is within 0.6 degrees of 36.6°C.
Lesson 2-3
Lesson 1-3
169-172
Solve each equation.
89. 3t + 4t = -21
90. 9(-2n + 3) = -27
91. k + 5 - 4k = -10
92. 5x + 3 - 2x = -21
93. 5.4m - 2.3 = -0.5
94. 3(y - 4) = 9
Write each group of numbers from least to greatest.
95. 3, -2, 0, -2.5, p
4
96. 15
2 , -1.5, 23, 7, -2
97. 0.001, 0.01, 0.009, 0.011
98. –p, 2p, –2.5, –3, 3
Chapter 3 Solving Inequalities