C Challenge

Solve each equation for x.

82. | a x | − b = c vertical line eh x vertical line negative b equals c
83. | c x − d | = a b vertical line c x minus d vertical line equals eh b
84. a | b x − c | = d eh vertical line b x minus c vertical line equals d

Graph each solution.

85. | x | ≥ 5 vertical line x vertical line greater than or equal to 5  and | x | ≤ 6 vertical line x vertical line less than or equal to 6
86. | x | ≥ 6 vertical line x vertical line greater than or equal to 6  or | x | < 5 vertical line x vertical line less than 5
87. | x − 5 | ≤ x vertical line x minus 5 vertical line less than or equal to x
88. Writing Describe the difference between solving | x + 3 | > 4 vertical line x plus 3 vertical line greater than 4  and | x + 3 | < 4 . vertical line x plus 3 vertical line less than 4 .
89. Reasoning How can you determine whether an absolute value inequality is equivalent to a compound inequality joined by the word and or one joined by the word or?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

90. What is the positive solution of |3x + 8| = 19?
91. If p is an integer, what is the least possible value of p in the following inequality? | 3 p − 5 | ≤ 7 vertical line 3 p minus 5 vertical line less than or equal to 7
92. In wood shop, you have to drill a hole that is 2 inches deep into a wood panel. The tolerance for drilling a hole is described by the inequality | t − 2 | ≤ 0.125. vertical line t minus 2 vertical line less than or equal to , 0.125.  What is the shallowest hole allowed?
93. The normal thickness of a metal structure is shown. It expands to 6.54 centimeters when heated and shrinks to 6.46 centimeters when cooled down. What is the maximum amount in cm that the thickness of the structure can deviate from its normal thickness?

    

Mixed Review

See Lesson 1-5.

Solve each inequality. Graph the solution.

94. 5 y − 10 < 20 5 y minus 10 less than 20
95. 15 ( 4 s + 1 ) < 23 15 open 4 s plus 1 close less than 23
96. 4 a + 6 > 2 a + 14 4 eh plus 6 greater than 2 eh plus 14

See Lesson 1-1.

Describe each pattern using words. Draw the next figure in each pattern.

97. 
    Image Long Description
98. 
    Image Long Description

Get Ready! To prepare for Lesson 2-1, do Exercises 99–102.

See p. 969.

Graph each ordered pair on the coordinate plane.

99. ( − 4 , − 8 ) open negative 4 comma negative 8 close
100. (3, 6)
101. (0, 0)
102. ( − 1 , 3 ) open negative 1 comma 3 close

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