C Challenge

64. Reasoning If | x | > | y | , vertical line x vertical line greater than vertical line y vertical line comma  does | x − y | = | x | − | y | ? vertical line x minus y vertical line equals vertical line x vertical line negative vertical line y vertical line question mark  Justify your answer.
65. Reasoning A student wrote the equation − | m | = | − m | . negative vertical line m vertical line equals vertical line negative m vertical line .  Is the equation always, sometimes, or never true? Explain.

Simplify each expression.

66. c 4 − c 4 c over 4 , minus , c over 4
67. w 5 + ( − w 10 ) w over 5 , plus . open , negative , w over 10 , close
68. d 5 − ( − d 5 ) d over 5 , minus . open , negative , d over 5 , close
69. Reasoning Answer each question. Justify your answers.
    1. Is | a − b | absolute value of eh minus b , end absolute value ,  always equal to | b − a | ? vertical line b minus eh vertical line question mark
    2. Is | a + b | absolute value of eh plus b , end absolute value ,  always equal to | a | + | b | ? vertical line eh vertical line plus vertical line b vertical line question mark

Standardized Test Prep

SAT/ACT

70. What is the value of − b − a negative b minus eh  when a = − 4  and  b = 7 ? eh equals negative 4 , and , b equals 7 question mark
    1. − 11 negative 11
    2. − 3 negative 3
    3. 3
    4. 11
71. Which expression is equivalent to 19 − 41 ? 19 minus 41 question mark
    6. | 19 − 41 | absolute value of 19 minus 41 , end absolute value ,
    7. | 19 + 41 | absolute value of 19 plus 41 , end absolute value ,
    8. − | 19 − 41 | negative vertical line 19 minus 41 vertical line
    9. − | 19 + 41 | negative vertical line 19 plus 41 vertical line
72. Which equation illustrates the Identity Property of Multiplication?
    1. x · 0 = 0 x middle dot 0 equals 0
    2. x · 1 = x x middle dot 1 equals x
    3. x ( y z ) = ( x y ) z x open y z close equals open x y close z
    4. x · y = y · x x middle dot y equals y middle dot x
73. What is an algebraic expression for the perimeter of the triangle?

    

    6. 8 + x
    7. 4x
    8. 8
    9. 4 + x

74. Which point on the number line below is the best estimate for 8 ? square root of 8 question mark

    

    1. P
    2. Q
    3. R
    4. S

Mixed Review

See Lesson 1-4.

Tell whether the expressions in each pair are equivalent.

75. 3 4 · d · 4  and  3 d 3 fourths , middle dot d middle dot 4 , and , 3 d
76. ( 2.1 · h ) · 3  and  6.3 + h open 2.1 middle dot h close middle dot 3 , and , 6.3 plus h
77. (6 + b) + a and 6 + (a + b)

See Lesson 1-3.

Name the subset(s) of real numbers to which each number belongs.

78. 1 3 1 third
79. − 5.333 negative , 5.333
80. 16 square root of 16
81. 82.0371
82. 21 square root of 21

Get Ready! To prepare for Lesson 1-6, do Exercises 83–85.

See Lesson 1-2.

Evaluate each expression for a = 2, h = 5, and w = 8.

83. 4 h − 5 a ÷ w 4 h minus 5 eh divides w
84. a 2 w − h 2 + 2 h eh squared , w minus , h squared , plus 2 h
85. ( w 2 h − a 2 ) + 12 ÷ 3 a open , w squared , h minus , eh squared , close plus 12 divides 3 eh

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