Page 97

miller_introductory_algebra_3e_ch1_3

Section 2.2 Solving Linear Equations 139 Concept 3: Conditional Equations, Identities, and Contradictions For Exercises 59–64, identify the equation as a conditional equation, a contradiction, or an identity. Then describe the solution. (See Example 8.) 59. 60. 61. 21k 72 2k 13 5h 4 51h 12 1 7x 3 61x 22 Contradiction; no solution Identity; all real numbers Conditional equation; 15 62. 3y 1 1 3y 63. 3 5.2p 5.2p 3 64. 21q 32 4q q 9 Contradiction; no solution Identity; all real numbers Conditional equation; 5 One solution Infinitely many solutions Mixed Exercises For Exercises 69–92, find the solution, if possible. 1 2 69. 70. 10 71. 2k 9 8 4p 6 8 2p 7 t 2 3 72. 31y 22 5 5 2 73. 71w 22 14 3w 74. 0.24 0.4m 1 2 0 0.6 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. No solution 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? Conditional equation 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 1y 52 4 4 314p 12 8 0.41a 202 6 81. 82. 83. 2.2r 12 3.4 1012n12 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 5 is a solution for x in the equation x a 10 . Find the value of a. 95. Suppose 3 is a solution for x in the equation ax 12 . Find the value of a. 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 6 is a solution for x in the equation x a 12 . Find the value of a. 96. Suppose 11 is a solution for x in the equation ax 49.5 . Find the value of a. 98. Write an equation that is a contradiction. Answers may vary. All real numbers 3 4 13 2 5 4 46 No solution 2 28 5 7 No solution All real numbers 20 2.205 10 4 1 0 3 a 4.5 For example: 4x 3 4x 1 a 15 a 4 For example: 5x 2 2 5x a 18 Writing     Translating Expression     Geometry      Scientific Calculator     Video


miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above