177 1.7 Inequalities 11. Explain how to determine whether to use a parenthesis or a square bracket when writing the solution set of a linear inequality in interval notation. 12. Concept Check The three-part inequality a 6x 6b means “a is less than x, and x is less than b.” Which inequality is not satisfied by some real number x? A. -3 6x 610 B. 0 6x 66 C. -3 6x 6 -1 D. -8 6x 6 -10 Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 13. -2x + 8 … 16 14. -3x - 8 … 7 15. -2x - 2 … 1 + x 16. -4x + 3 Ú -2 + x 17. 31x + 5 + 1 Ú 5 + 3x 18. 6x - 12x + 32 Ú 4x - 5 19. 8x - 3x + 2 621x + 72 20. 2 - 4x + 51x - 12 6 -61x - 22 21. 4x + 7 -3 … 2x + 5 22. 2x - 5 -8 … 1 - x 23. 1 3 x + 2 5 x - 1 21x + 32 … 1 10 24. - 2 3 x - 1 6 x + 2 31x + 12 … 4 3 Break-Even Interval Find all intervals where each product will at least break even. See Example 3. 25. The cost to produce x units of picture frames is C = 50x + 5000, while the revenue is R = 60x. 26. The cost to produce x units of baseball caps is C = 100x + 6000, while the revenue is R = 500x. 27. The cost to produce x units of coffee cups is C = 105x + 900, while the revenue is R = 85x. 28. The cost to produce x units of briefcases is C = 70x + 500, while the revenue is R = 60x. Solve each inequality. Give the solution set in interval notation. See Example 4. 29. -5 65 + 2x 611 30. -7 62 + 3x 65 37. -3 … 3x - 4 -5 64 38. 1 … 4x - 5 -2 69 33. -11 7 -3x + 1 7 -17 34. 2 7 -6x + 3 7 -3 31. 10 … 2x + 4 … 16 32. -6 … 6x + 3 … 21 35. -4 … x + 1 2 … 5 36. -5 … x - 3 3 … 1 39. x2 + 3x - 4 60 40. x2 - 7x + 10 60 43. 2x2 - 9x … 18 44. 3x2 + x … 4 51. x2 + 5x + 7 60 52. 4x2 + 3x + 1 … 0 Solve each quadratic inequality. Give the solution set in interval notation. See Examples 5 and 6. 41. x2 - x - 6 70 42. x2 - 7x + 10 70 45. -x2 - 4x - 6 … -3 46. -x2 - 6x - 16 7 -8 53. x2 - 2x … 1 54. x2 + 4x 7 -1 47. x1x - 12 … 6 48. x1x + 12 612 49. x2 … 9 50. x2 716
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