130 Chapter 2 Linear Equations and Inequalities Concept 3: Multiplication and Division Properties of Equality For Exercises 35–54, solve the equations using the multiplication or division property of equality. Be sure to check your answers. (See Examples 4–7.) 35. 6x 54 9 36. 2w 8 4 37. 12 3p 4 38. 6 2q 3 y 5 39. 5y 0 0 40. 3k 0 0 41. 3 15 42. 7 4 5 43. 44. 45. 10 46. 24 4 3 3 10 2 5 47. 4 48. w 49. 41 x 41 50. 32 y 32 51. 3.81 0.03p 52. 2.75 0.5q 53. 5.82y 15.132 54. 32.3x 0.4522 Concept 4: Translations For Exercises 55–64, write an algebraic equation to represent each English sentence. (Let x represent the unknown number.) Then solve the equation. (See Example 8.) 61. The quotient of a number and twelve is one-third. 62. Eighteen is equal to the quotient of a number and two. x 12 1 3 ; The number is 4. 63. The sum of a number and is 13. 8 58 2 3 18 x 2 ; The number is 36. 64. The difference of a number and is . 13 x 5 8 13 8 ; The number is 1. x 2 3 1 3 ; The number is 1. Mixed Exercises For Exercises 65–88, solve the equation using the appropriate property of equality. 65. a. a 9 1 10 66. a. k 2 4 2 67. a. h 8 12 68. a. 20 1 9 b. b. 2 3 4 2 3 p 15 p 15 22 3 2 3 b. b. 2k 4 d 4 r 3 57 4 3 4 h 8 9a 1 69. 36 70. 20 71. k 16 32 16 72. 18 9 t 9 7 4 5 12 73. 2 74. 2 75. 76. 3s 10 2 5 16k 32 18 9t 7 4q 1 3 10 3 77. 4 q 7 11 78. s 3 10 13 79. d 12 36 80. m 10 25 1.2y 4.8 4 4.3w 8.6 2 11 4 1 4 p 7 2 1 2 81. 4 z 82. 3 83. 84. 85. 4.8 1.2 y 3.6 86. 8.6 w 4.3 12.9 87. 0.0034 y 0.405 88. 0.98 m 1.0034 Writing Translating Expression Geometry Scientific Calculator Video 1 5 b 4 5 3 8 b 9 2 5 a 4 3 7 3 7 h 4 5 t z 7 1 127 5.5 2.6 0.014 55. The sum of negative eight and a number is forty-two. 8 x 42; The number is 50. 56. The sum of thirty-one and a number is thirteen. 31 x 13; The number is 18. 57. The difference of a number and negative six is eighteen. x 162 18; The number is 12. 58. The sum of negative twelve and a number is negative fifteen. 12 x 15; The number is 3. 59. The product of a number and seven is the same as negative sixty-three. x 7 63 or 7x 63; The number is 9. 60. The product of negative three and a number is the same as twenty-four. 3x 24; The number is 8. 0.4084 1.9834
miller_introductory_algebra_3e_ch1_3
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