Section 1.7 Absolute Value Inequalities 103 04x 1 0 0 3x 4 0 6 04p 0 8 03q 0 0 0 19. 20. 21. 22. ` ` 2 7 7z 3 23. 24. 25. 26. 1 4 27. 28. 29. 30. 3 05x 1 0 2 03b 7 0 4 4 1 9 9 10 4 05x 7 0 02y 1 0 31. 32. 33. 34. 7 04k 6 0 0 7 06x 9 0 3 0x 5 0 2 0x 3 0 7 5 35. 36. 37. 38. 1 6 39. 40. 41. 42. Concept 2: Solving Equations Containing Two Absolute Values For Exercises 43–60, solve the absolute value equations. (See Examples 6–7.) 43. 44. 45. 46. 47. 48. 04w 3 0 03x 5 0 02w 5 0 004x 2 0 5 0 08 0 09a 5 0 02y 5 0 09a 1 0 03y 1 0 07 2y 0 02y 7 0 0x 2 0 0` x 2 0 6p 3 ` p 2 ` 4w 1 49. 50. 51. 011.2n 9 0 03.5m 1.2 0 07.2n 2.1 0 02y 3 0 08.5m 6 0 02y 3 0 52. 53. 54. 55. 56. 57. 58. 59. 60. Expanding Your Skills 08 7w0 07w 8 0 03 6y 0 04x 3 0 08 2y 0 02x 1 0 0t 6 0 0t 1 0 0x 2 0 0 0x 4 0 04 3z 0 0 03z 4 0 72 43 Absolute Value Inequalities Section 1.7 1. Solving Absolute Value Inequalities by Definition In Section 1.6, we studied absolute value equations in the form In this section, we will solve absolute value inequalities. An inequality in any of the forms Concepts 1. Solving Absolute Value Inequalities by Definition 2. Solving Absolute Value Inequalities by the Test Point Method 3. Translating to an Absolute Value Expression 0x 0 0x 0 a 0x 0 6 a, a, 0x 0 7 a, or is called an absolute value inequality. Recall that an absolute value represents distance from zero on the real number line. Consider the following absolute value equation and inequalities. 1. 0x 0 3 x 3 or x 3 0x 0 a. 8 ` ` 3 4 6 ` ` 2w 3 1 4 ` ` 3 02 6x 0 5 10 5 01 2x 0 7 3 2 9 h ` 1 2 ` 1 5 1 2 k ` 9 5 12 6 1 4 06 2x 0 ` 2 01.81 2x 0 w ` 00.2x 3.5 0 2.2 5.6 ` w 2 3 2 1 3 ` 10 3 6 5 0 3x 7 0 0 2x 4 0 61. Write an absolute value equation whose solution is the set of real numbers 6 units from zero on the number line. 62. Write an absolute value equation whose solution is the set of real numbers units from zero on the number line. 63. Write an absolute value equation whose solution is the set of real numbers units from zero on the number line. 64. Write an absolute value equation whose solution is the set of real numbers 9 units from zero on the number line. Solution: The set of all points 3 units from zero on the number line 1 2 3 4 5 6 3 units 6 54 3 2 1 0 3 units
miller_intermediate_algebra_4e_ch1_3
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