Name
Class
1-6
Date
Practice
Form K
Absolute Value Equations and Inequalities
Solve each equation. Check your answers. Graph the solution.
1. u 22x u 5 12
2. u 7y u 5 28
Solve each equation. Check your answers.
3. u t 1 7 u 5 1
t 1 7 5 1 or t 1 7 5 21
To start, rewrite the absolute value
equation as two equations.
4. 4 u z 1 1 u 5 24
5. u 2w 1 1 u 5 5
6. u 2x 2 2 u 5 4
7. u 5 2 2y u 1 3 5 8
Solve each equation. Check for extraneous solutions.
8. u 2z 2 9 u 5 z 2 3
To start, rewrite as two equations.
2z 2 9 5 z 2 3 or 2z 2 9 5 2(z 2 3)
9. u x 1 6 u 5 2x 2 3
10. u 2t 2 5 u 5 3t 2 10
11. 2 u 4y 1 1 u 5 4y 1 10
12. u w 1 1 u 2 5 5 2w
Write an absolute value equation to describe each graph.
13.
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
1
2
3
14.
4
⫺5 ⫺4 ⫺3 ⫺2 ⫺1
Is the absolute value equation always, sometimes, or never true? Explain.
15. u w u 5 22
16. u z u 1 1 5 z 1 1
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0
Name
1-6
Class
Date
Practice (continued)
Form K
Absolute Value Equations and Inequalities
Solve each inequality. Graph the solution.
17. 2 u x 1 5 u # 8
ux 1 5u # 4
To start, divide each side by 2.
x 1 5 is greater than or equal to 24 and less than or equal to 4.
24 # x 1 5 # 4
18. u x 1 1 u 2 3 # 1
19. u 2z 1 2 u 2 1 . 3
20. 2 u w 1 3 u 2 1 , 1
21. u y 2 3 u 1 2 $ 4
22. u 2t 1 2 u 1 5 # 9
23. u 2s 1 1 u . 3
Write each compound inequality as an absolute value inequality.
24. 1.2 # a # 2.4
To start, find the tolerance.
2.4 2 1.2
1.2
5 2 5 0.6
2
25. 22 , x , 4
26. 1 # m # 2
27. 20 # y # 30
28. 23 , t , 17
Write an absolute value inequality to represent each situation.
29. In order to enter the kiddie rides at the amusement park, a child must be
between the ages of 4 and 10. Let a represent the age of a child who may go
on the kiddie rides.
30. The outdoor temperature ranged between 42°F and 60°F in a 24-hour period.
Let t represent the temperature during this time period.
Prentice Hall Foundations Algebra 2 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
56