C Challenge

Solve each equation. Check your solutions.

77. | x + 4 | = 3x
78. | 4 t − 5 | = 2 t + 1 vertical line 4 t minus 5 vertical line equals 2 t plus 1
79. 4 3 | 2 y + 3 | = 4 y 4 thirds , vertical line 2 y plus 3 vertical line equals 4 y

Determine whether each statement is always, sometimes, or never true for real numbers a and b.

80. | a b | = | a | · | b | absolute value of eh b vertical line equals vertical line eh vertical line middle dot vertical line b , end absolute value ,
81. | a b | = | a | | b | , b ≠ 0 absolute value of , eh over b , end absolute value , . equals . fraction absolute value of eh , , over absolute value of b , end fraction . comma b not equal to 0
82. | a + b | = | a | + | b |

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

83. The expected monthly rainfall in a certain town is shown for June, July, and August. The actual rainfall generally varies from the expected amount by up to 0.015 in. What is the maximum amount of rainfall the town can expect to receive in July?

    Expected Monthly Rainfall (inches)

    June	July	August
    4.12	4.25	4.41

84. What is the solution of the equation x 4 − 3 = 7 ? x over 4 , minus 3 equals 7 question mark
85. What is the solution of the equation 3 w + 2 = 4 w − 3 ? 3 w plus 2 equals 4 w minus 3 question mark
86. Jose is purchasing 4 dress shirts that cost $28 each and 2 pairs of pants that cost $38 each. The items are all on sale for 35% off. How much money will Jose save by purchasing them on sale instead of at full price?
87. 75% of what number is 90?

Mixed Review

See Lesson 3-6.

Write a compound inequality to model each situation.

88. The highest elevation in North America is 20,320 ft above sea level at Mount McKinley, Alaska. The lowest elevation in North America is 282 ft below sea level at Death Valley, California.
89. Normal human body temperature T is within 0.3°C of 37.2°C.

See Lesson 1-7.

Simplify each expression.

90. 2(x + 5)
91. − 3 ( y − 7 ) negative 3 open y minus 7 close
92. 4 ( ℓ + 3 ) − 7 4 open script l plus 3 close minus 7
93. − ( m − 4 ) + 8 negative open m minus 4 close plus 8

Get Ready! To prepare for Lesson 3-8, do Exercises 94–97.

See Lesson 3-5.

Write each set in set-builder notation.

94. A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
95. B = {1, 3, 5, 7}

Write each set in roster form.

96. C = {n | n is an even number between − 15 negative 15  and − 5 negative 5 }
97. D = {k | k is a composite number between 7 and 17}

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