Posted: November 5th, 2015

Absolute Value Equations and Inequalities

Absolute Value Equations and Inequalities

Practice 1-5 Absolute Value Equations and Inequalities
Write each specification as an absolute value inequality.
1. 6.3
h
10.3 2. -2.5
a
2.5 3. 22
x
33
Solve each inequality. Graph the solutions.
4. ?x + 5«  12 5. ?k – 3«
19 6. ?x + 2«  0
7. 2?t – 5«  14 8. ?3x – 2« + 7  11 9. 5?2b + 1« – 3
7
10. ?2 – 3w«  4 11. -3?7m – 8«  5 12. ?2u«  6
Solve each equation. Check for extraneous solutions.
13. ?4x« = 28 14. ?3x + 6«=-12 15. ?z – 1« = 7z – 13
16. ?s + 12« = 15 17. ?-3x« = 63 18. 2?5x + 3« = 16
19. ?6x + 7« = 5x + 2 20. ?7r – 4« = 24 21. ?3c« + 2 = 11
22. 5?x + 1« + 6 = 21 23. ?3x + 5« – 2x = 3x + 4 24. -?d + 2« = 7
Write an absolute value inequality and a compound inequality for each
length x with the given tolerance.
25. a length of 4.2 cm with a tolerance of 0.01 cm
26. a length of 3.5 m with a tolerance of 0.2 cm
27. a length of 10 ft with a tolerance of 1 in.
28. Write an absolute value inequality and a compound inequality for the
temperature T that was recorded to be as low as 65°F and as high as
87°F on a certain day.
29. The weight of a 40-lb bag of fertilizer varies as much as 4 oz from the
stated weight. Write an absolute value inequality and a compound
inequality for the weight w of a bag of fertilizer.
30. The duration of a telephone call to a software company’s help desk is
at least 2.5 minutes and at most 25 minutes. Write an absolute value
inequality and a compound inequality for the duration d of a
telephone call.

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