120 Chapter 2 Linear Equations and Inequalities 23 14p 12 13p 12 4 513 p2 9 5 16k 12 23 15k 32 1k 22 4 55. 56. 310.9n 0.52 3.5n 1.3 710.4m 0.12 5.2m 0.86 57. 58. Concept 3: Conditional Equations, Identities, and Contradictions For Exercises 59–64, solve each equation. Identify as a conditional equation, an identity, or a contradiction. (See Example 8.) 59. 21k 72 2k 13 60. 5h 4 51h 12 1 61. 7x 3 61x 22 62. 3y 1 1 3y 63. 3 5.2p 5.2p 3 64. 21q 32 4q q 9 65. A conditional linear equation has (choose one): one solution, no solution, or infinitely many solutions. 66. An equation that is a contradiction has (choose one): one solution, no solution, or infinitely many solutions. 67. An equation that is an identity has (choose one): one solution, no solution, or infinitely many solutions. 68. If the only solution to a linear equation is 5, then is the equation a conditional equation, an identity, or a contradiction? Mixed Exercises For Exercises 69–92, solve each equation. 1 2 69. 70. 71. 2k 9 8 4p 6 8 2p t 2 3 31y 22 5 5 71w 22 14 3w 0.24 0.4m 72. 73. 74. 1 4 1 2 21x 22 3 2x 1 75. 76. 77. n 0.5b 23 312r 12 61r 22 6 8 2q 4 3 1 78. 79. 80. x 7 2 4 4 314p 12 8 0.41a 202 6 1 y 52 4 81. 82. 83. 2.2r 12 3.4 1012n 12 6201n12 12 y 5 3 84. 85. 86. 87. 88. 89. 2 5 6g 8 4 3g 8 13q 42 6 q 6w 18 2w2 21w 42 90. 91. 92. Expanding Your Skills 93. Suppose the solution set for x in the equation is {5}. Find the value of a. x a 10 95. Suppose the solution set for x in the equation is {3}. Find the value of a. ax 12 97. Write an equation that is an identity. Answers may vary. 4 5 t 1 1 5 c 0.123 2.328 412z 32 81z 32 36 t 5 94. Suppose the solution set for x in the equation is {6}. Find the value of a. x a 12 96. Suppose the solution set for x in the equation is {11}. Find the value of a. ax 49.5 98. Write an equation that is a contradiction. Answers may vary.
miller_beginning_intermediate_algebra_4e_ch1_3
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