C Challenge

Open-Ended Write an inequality with a solution that matches the graph. At least two steps should be needed to solve your inequality.

62. 
63. 
64. 
65. 
66. Reasoning Consider the compound inequality x < 8 x less than 8  and x > a . x greater than eh .
    1. Are there any values of a such that all real numbers are solutions of the compound inequality? If so, what are they?
    2. Are there any values of a such that no real numbers are solutions of the compound inequality? If so, what are they?
    3. Repeat parts (a) and (b) for the compound inequality x < 8 x less than 8  or x > a . x greater than eh .

Standardized Test Prep

SAT/ACT

67. What is the solution of 1 < 2 x + 3 < 9 ? 1 less than 2 x plus 3 less than 9 question mark
    1. − 1 > x < 2 negative 1 greater than x less than 2
    2. 2 < x < 3 2 less than x less than 3
    3. − 1 < x < 2 negative 1 less than x less than 2
    4. − 1 < x < 3 negative 1 less than x less than 3
68. Which expression best represents the value of x in y = mx + b?
    6. b − y m fraction b minus y , over m end fraction
    7. y + b m fraction y plus b , over m end fraction
    8. m ( y − b ) m open y minus b close
    9. y − b m fraction y minus b , over m end fraction
69. The hourly rate of a waiter is $4 plus tips. On a particular day, the waiter worked 8 hours and received more than $150 in pay. Which could be the amount of tips the waiter received?
    1. $18.75
    2. $32
    3. $118
    4. $120.75

Extended Response

70. Solve 3 ( x − 2 ) + 8 = 12 . 3 open x minus 2 close plus 8 equals 12 .  Identify each property of real numbers or equality you use.

Mixed Review

See Lesson 1-3.

Simplify each expression.

71. ( 2 a − 4 ) + ( 5 a + 9 ) open 2 eh minus 4 close plus open 5 eh plus 9 close
72. 3 ( x + 3 y ) − 5 ( x − y ) 3 open x plus 3 y close minus 5 open x minus y close
73. 1 3 ( b + 12 ) − 1 4 ( b + 12 ) 1 third . open , b plus 12 , close . minus , 1 fourth . open , b plus 12 , close
74. 0.4 ( k − 0.1 ) + 0.5 ( 3.3 − k ) 0.4 open k minus 0.1 close plus 0.5 open 3.3 minus k close

Get Ready! To prepare for Lesson 1-6, do Exercises 75–78.

See Lesson 1-4.

Solve each equation. Check your answers.

75. 7 x − 6 ( 11 − 2 x ) = 10 7 x minus 6 open 11 minus 2 x close equals 10
76. 10 x − 7 = 2 ( 13 + 5 x ) 10 x minus 7 equals 2 open 13 plus 5 x close
77. 4 y − 1 10 = 3 y + 4 5 4 y minus , 1 tenth , equals 3 y plus , 4 fifths
78. 0.4 x + 1.18 = − 3.1 ( 2 − 0.01 x ) 0.4 x plus , 1.18 , equals negative 3.1 open 2 minus , 0.01 , x close

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