Section 2.7 Absolute Value Inequalities 135 SECTION 2.7 EXERCISE SET Write About It! Use complete sentences in your answer to each exercise. 1. Explain how to solve an absolute value inequality involving a less than symbol. 2. Explain how to solve an absolute value inequality involving a greater than symbol. 3. Describe the special cases that may arise when solving an absolute value inequality. 4. Use an example to explain how to use test points to solve an absolute value inequality, ux - au < b, b > 0. 5. Use an example to explain how to use test points to solve an absolute value inequality, ux - au > b, b > 0. 6. Use an example to explain how to solve an absolute value inequality, ux - au ≤ 0. Practice Makes Perfect! Solve each inequality. Write each answer in interval notation. (See Objective 1.) 7. uxu ≤ 6 8. uxu ≤ 3 9. uy - 4u < 19 10. uy + 6u < 20 11. u2x + 3u < 4 12. u4x - 3u < 5 13. u3x - 1u ≤ 6 14. u6x - 7u ≤ 12 15. u2 - 5xu < 1 16. u6 - 3xu < 7 17. u1 - 4xu ≤ 5 18. u3 - 9xu ≤ 15 19. u3x - 1u + 5 < 12 20. u5x + 3u + 8 < 10 21. u7 + 4xu - 1 < 4 22. u6 - 2xu - 8 < 3 23. 6 + u8x - 5u ≤ 16 24. 5 + u3x + 2u < 15 Solve each inequality. Write each answer in interval notation. (See Objective 2.) 25. uyu > 4 26. uyu > 9 27. ux - 3u ≥ 2 28. ux + 7u ≥ 12 29. u5x + 5u > 17 30. u6x + 7u > 8 31. u10x - 4u > 16 32. u8x - 3u > 13 33. u8 - 4xu > 6 34. u7 - 3xu > 5 35. u2x + 7u - 3 ≥ 6 36. u3x - 5u - 9 ≥ 1 37. u6 - 2xu + 3 ≥ 11 38. u7 - 4xu + 6 ≥ 13 39. 4 + u6x - 1u > 9 40. 7 + u2x + 9u > 15 Solve each inequality. Write each answer in interval notation. (See Objective 3.) 41. uau ≤-1 42. uau ≤-5 43. ux + 5u < 0 44. u3x - 6u < 0 45. ` x + 1 2 ` < 0 46. ` 2x - 3 5 ` < 0 47. u2x + 5u + 6 ≤ 3 48. u5x - 1u + 8 ≤ 2 49. uxu >-8 50. uxu >-2 51. u4x + 10u > 0 52. u5x - 6u > 0 53. u3x - 18u ≤ 0 54. u15 - 5xu ≤ 0 55. ` 4x - 3 2 ` > 0 56. ` x + 3 4 ` > 0 57. u4 - 3xu + 6 ≤ 3 58. u2 - 7xu + 9 ≤ 6 59. u7 - xu ≤ 0 60. u6 - 2xu ≤ 0 61. 5 + u4x + 6u > 5 62. 1 + u2x + 5u > 1 63. ` 3x - 1 5 ` + 4 > 6 64. ` 2x + 5 3 ` - 1 ≥ 3 65. ` 5x + 3 2 ` - 3 ≤ 1 66. ` x - 4 6 ` + 3 < 8 so they are included in the solution set. So, the solution set is -7, 1. The TABLE also shows a picture of the solution set. The x-values whose y-value is 1 are part of the solution of the inequality. The x-values whose y-value is 0 are not solutions of the inequality. The table confirms the solution -7, 1.
hendricks_intermediate_algebra_1e_ch1_3
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