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Name
Class
1-6
Date
Practice
Form G
Absolute Value Equations and Inequalities
Solve each equation. Check your answers.
1. u23x u 5 18 x 5 6 or x 5 26
2. u 5y u 5 35 y 5 7 or y 5 27
3. u t 1 5 u 5 8 t 5 3 or t 5 213
4. 3u z 1 7 u 5 12 z 5 23 or z 5 211
5. u 2x 2 1 u 5 5 x 5 3 or x 5 22
6. u 4 2 2y u 1 5 5 9 y 5 4 or y 5 0
Solve each equation. Check for extraneous solutions.
7. u x 1 5 u 5 3x 2 7 x 5 6
8. u 2t 2 3 u 5 3t 2 2 t 5 1
5
9. u 4w 1 3 u 2 2 5 5 w 5 1 or w 5 22
10. 2u z 1 1 u 2 3 5 z 2 2
z 5 21
Solve each inequality. Graph the solution.
11. 5u y 1 3 u , 15 26 R y R 0
⫺8 ⫺6 ⫺4 ⫺2
0
2
12. u 2t 2 3 u # 5 21 K t K 4
⫺2 ⫺1
4
1
14. 2 u 2w
13. u 4b u 2 3 . 9 b < 23 or b > 3
⫺9 ⫺6 ⫺3
0
3
6
0
1
2
1
2
3
4
2 1u 2 3 $ 1 w K 272 or w L
⫺6 ⫺4 ⫺2
9
1
15. 2u 4x 1 1 u 2 5 # 1 21 K x K 2
⫺3 ⫺2 ⫺1
0
0
2
4
9
2
6
2
16. u 3z 2 2 u 1 5 . 9 z R 23 or z S 2
⫺3 ⫺2 ⫺1
3
0
1
2
3
Write each compound inequality as an absolute value inequality.
17. 27.3 # a # 7.3 »a» K 7.3
18. 11 # m # 19 »m 2 15» K 4
19. 28.6 # F # 29.2 »F 2 28.9» K 0.3
20. 0.0015 # t # 0.0018 »t 2 0.00165» K 0.00015
Write an absolute value equation or inequality to describe each graph.
21.
⫺6 ⫺4 ⫺2
0
2
4
22.
6
»x» 5 6
⫺3 ⫺2 ⫺1
0
1
»x» S 2.5
Prentice Hall Gold Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
53
2
3
Name
1-6
Class
Practice
Date
Form G
(continued)
Absolute Value Equations and Inequalities
Solve each equation.
23. 3u 2x 1 5 u 5 9x 2 6 x 5 7
3
24. u 4 2 3m u 5 m 1 10 m 5 7 or m 5 2 2
25. 2u 4w 2 5 u 5 12w 2 18 w 5 2
3
26. 4 u8t 2 12 u 5 6(t 2 1) t 5 5
4
27. u 5p 1 3 u 2 4 5 2p p 5 13 or p 5 21
28. u 7y 2 3 u 1 1 5 0 no solution
Solve each inequality. Graph the solution.
29. 23u 2t 1 1 u , 9 all real numbers
30. u 22x 1 4 u $ 4 x K 0 or x L 4
0
⫺3 ⫺2 ⫺1
y 1 2
31. ` 3 ` 2 1 , 2
1
1
32. 7 u 4z 1 5 u 1 2 . 5
⫺16 ⫺12 ⫺8 ⫺4
0
2
⫺1
3
211 R y R 7
4
0
1
⫺9 ⫺6 ⫺3
8
2
0
3
3
4
5
z R 213
2 or z S 4
6
9
Write an absolute value inequality to represent each situation.
33. To become a potential volunteer donor listed on the National Marrow Donor
Program registry, a person must be between the ages of 18 and 60. Let a
represent the age of a person on the registry. »a 2 39» K 21
34. Two friends are hiking in Death Valley National Park. Their elevation ranges
from 228 ft below sea level at Badwater to 690 ft above sea level at Zabriskie
»x 2 231» K 459
Point. Let x represent their elevation.
35. The outdoor temperature ranged between 37°F and 62°F in a 24-hour period.
Let t represent the temperature during this time period. »t 2 49.5» K 12.5
The diameter of a ball bearing in a wheel assembly must be between 1.758 cm and
1.764 cm.
36. What is the tolerance? 0.003 cm
37. What absolute value inequality represents the diameter of the ball bearing?
Let d represent the diameter in cm. »d 2 1.761» R 0.003
Prentice Hall Gold Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
54