Inequalities



Absolute Value Equations

Solve and graph the solution each of the following equations. Write the solution in interval notation.

Set 1

1. |2x+ 3| = 5 2. |3 – x| = 7

3. |4x – 3| = 13 4. |5 – 3x| = 2

5. = 5 6. = 2

7. 3 – |5x – 2| = –7 8. – =

9. – 3 = 10. 4 – 2|4 – 3x| = –8

11. |5x + 3| = |2x – 1| 12. |2 + 3x| = |4 – 2x|

13. |3x – 4| = |2x + 3| 14. =

15. = 16. =

Set 2

1. | x | < 3 2. | x | ≤ 8

3. | 2x | < 6 4. ≤ 5

5. | x + 3 | < 4 6. | x – 2 | < 6

7. | x – 8 | < 12 8. <

9. < 10. <

11. | x – 1 | < 3 12. | x + 3 | ≤ 4

13. | 3x – 2 | < 9 14. < 1

15. | 2x + 5 | < 9 16. < 3

17. 1 + 2|x – 1| ≤ 9 18. 10 – 3|x – 2| ≥ 4

19. 6 – |2x – 5| ≥ 3 20. – 2 ≥ –

21. – 2 > –2 22. – 3 ≥ –

Set 3

1. | x | > 5 2. | 3x | > 5

3. > 4 4. | x – 4 | > 5

5. | x + 3 | ≥ 3 6. | 2x – 4 | > 6

7. | 3x – 5 | ≥ 3 8. ≥ 3

9. > 2 10. ≥ 3

11. 3 – |2 – x| < 1 12. 4 + 3|x – 1| ≥ 10

13. 3 – 2|3x – 1| ≥ –7 14. + ≥

15. – ≤ – 16. – < –

Answers

Set 1

1. –4, 1 2. 10, –4 3. 4, – 4. 1,

5. – , 6. –3, 7. , – 8. , –

9. , 10. , – 11. – , – 12. –6,

13. 7, 14. – , – 15. – , – 16. 0, –

Set 2

2. [–8, 8] 4. [–2, 2] 6. (–4, 8)

8. (– , 1) 10. (1, ) 12. [–7, 1]

14. (0, 4) 16. (–5, 4) 17. [–3, 5]

18. [0, 4] 19. [1, 4] 20. [–10, 2]

21. [–1, 3] 22.

Set 3

2. (–∞, – ) or (, ∞) 4. (–∞, –1) or (9, ∞) 6. (–∞, –1) or (5, ∞)

8. (–∞, –3] or [9, ∞) 10. (–∞, –2] or [7, ∞) 11. (–∞, 0) or (4, ∞)

12. (–∞, –1] or [3, ∞) 13. 14. (–∞, –1] or [0, ∞)

15. or [3. ∞) 16. or

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