185 1.8 Absolute Value Equations and Inequalities 1.8 Exercises CONCEPT PREVIEW Match each equation or inequality in Column I with the graph of its solution set in Column II. I 1. x = 7 2. x = -7 3. x 7 -7 4. x 77 5. x 67 6. x Ú 7 7. x … 7 8. x ≠7 II A. 0 –7 7 B. ∅ 0 –7 7 C. 0 –7 7 D. 0 –7 7 E. 0 –7 7 F. 0 –7 7 G. 0 –7 7 H. 0 –7 7 Solve each equation. See Example 1. 9. 3x - 1 = 2 10. 4x + 2 = 5 11. 5 - 3x = 3 12. 7 - 3x = 3 13. ` x - 4 2 ` = 5 14. ` x + 2 2 ` = 7 15. ` 5 x - 3 ` = 10 16. ` 3 2x - 1 ` = 4 17. ` 6x + 1 x - 1 ` = 3 18. ` 2x + 3 3x - 4 ` = 1 19. 2x - 3 = 5x + 4 20. x + 1 = 1 - 3x 21. 4 - 3x = 2 - 3x 22. 3 - 2x = 5 - 2x 23. 5x - 2 = 2 - 5x 24. The equation 5x - 6 = 3x cannot have a negative solution. Why? 25. The equation 7x + 3 = -5x cannot have a positive solution. Why? 26. Concept Check Determine the solution set of each equation by inspection. (a) - x = x (b) -x = x (c) x2 = x (d) - x = 9 Solve each inequality. Give the solution set in interval notation. See Example 2. 27. 2x + 5 63 28. 3x - 4 62 29. 2x + 5 Ú 3 30. 3x - 4 Ú 2 31. ` 1 2 - x ` 62 32. ` 3 5 + x ` 61 33. 4 x - 3 712 34. 5 x + 1 710 35. 5 - 3x 77 36. 7 - 3x 74 37. 5 - 3x … 7 38. 7 - 3x … 4 39. ` 2 3 x + 1 2 ` … 1 6 40. ` 5 3 - 1 2 x ` 7 2 9 41. 0.01x + 1 60.01 42. Explain why the equation x = 2x2 has infinitely many solutions.
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