140 Chapter 2 Linear Equations and Inequalities in One Variable SECTION 2.6 Absolute Value Equations 37. The absolute value of a number is its from zero on the number line. 38. The absolute value of any real number is . 39. If uXu = k, k > 0, then or . 40. If uXu = 0, then . 41. If uXu = k, k < 0, then there is . 42. To solve an absolute value equation, we must first the absolute value on one side of the equation. 43. If uXu = uYu, then or . That is, the expressions inside the absolute value must be the or . 44. The is the absolute value of the difference between the measured value and the exact value. SECTION 2.7 Absolute Value Inequalities 45. Solving uXu < k, k > 0 is equivalent to solving the compound inequality . This can be written in a compact form, . 46. Solving uXu > k, k > 0 is equivalent to solving the compound inequality . 47. If uXu < k, k < 0, then there is . 48. If uXu > k, k < 0, then the solution set is . 49. Another method to solve absolute value inequalities involves using . CHAPTER 2 / REVIEW EXERCISES SECTION 2.1 Determine if each equation is a linear equation. If so, determine if the given number is a solution of the equation. (See Objective 1.) 1. 3x - 2 (x + 5) = x - 4; x = 8 2. 4x + 3 - 8x = 3 - 4x; x=- 3 2 3. 4x + 3 7 = 1; x = 1 4. 2x - 3 10 =- 1 2 ; x=-1 Solve each equation. (See Objectives 2–4.) 5. 4x + 1 = 17 6. 5 - 3x=-10 7. n 6 =-2 8. 3 - t 4 =-5 9. 12.6 - d=-5.4 10. 26.8 - 2d = 12.4 11. -2.5 = 3x + 6.8 12. 3.6 = 2x - 9.4 13. 5y 3 + 1 6 = 3 2 14. 5y 6 - 2 3 = 1 2 15. 3(2x - 11) - 4(x - 7) = 5x + 10 16. 8(x - 2) - 2(1 - 3x) = 2(7x - 5) 17. 2(x - 9) - 3(2 - x) = 5x - 24 18. 7x + 5(3 - 2x)=-3(x - 5) SECTION 2.2 Translate each problem into a linear equation and find the solution. (See Objective 1.) 19. The sum of two consecutive even integers is 66. Find the integers. 20. The sum of two consecutive integers is 43. Find the integers. 21. Seven decreased by triple a number is -17. Find the number. 22. Twenty decreased by twice a number is -10. Find the number. 23. The quotient of a number and 4 is 7. Find the number. 24. The quotient of a number and 6 is 12. Find the number. 25. The product of a number and 1 3 is 48. Find the number. 26. The product of a number and 1 5 is 45. Find the number. 27. Nine less than twice times a number yields 21. Find the number. 28. Thirteen less than three times a number yields 17. Find the number. 29. The quotient of a number and 4 subtracted from the number is 9. Find the number. 30. The quotient of a number and 3 subtracted from the number is 20. Find the number. 31. Three times the sum of a number and 8 is 15. Find the number. 32. Twice the sum of a number and 4 is 24. Find the number. 33. Wesley saves quarters and dimes in a jar. If he has 18 more quarters than dimes and his collection is worth $16.05, how many quarters has Wesley saved? 34. George saves half-dollars and silver dollars. If he has 41 more half-dollars than silver dollars and his collection is worth $148, how many half-dollars has George saved? 35. The number of calories in a Burger King Whopper is 670 Cal. This is 220 Cal more than half the number
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