75. Banking To avoid a service fee, your checking account balance must be at least $500 at the end of each month. Your current balance is $536.45. You use your debit card to spend $125.19. What possible amounts can you deposit into your account by the end of the month to avoid paying the service fee?

C Challenge

Reasoning Decide whether each inequality is true for all real numbers. If the inequality is not true, give a counterexample.

76. x + y > x − y x plus y greater than x minus y
77. If x ≤ y , x less than or equal to y comma  then x + w ≤ y + w . x plus w less than or equal to y plus w .
78. If w < z , w less than z comma  then x − w > x − z . x minus w greater than x minus z .
79. If x > y , x greater than y comma  then x > y + w . x greater than y plus w .
80. Reasoning Find real numbers a, b, c, and d for which it is true that a < b eh less than b  and c < d , c less than d comma  but it is not true that a − c < b − d . eh minus c less than b minus d .

Standardized Test Prep

SAT/ACT

81. What is the solution of − 21 + p > 30 ? negative 21 plus p greater than 30 question mark
    1. p < 9 p less than 9
    2. p > 9 p greater than 9
    3. p < 51 p less than 51
    4. p > 51 p greater than 51
82. Richard won a 130-mi bike race. He finished in 11 h and 45 min. What was his average speed?
    6. 11.8 mi/h
    7. 11.4 mi/h
    8. 11.1 mi/h
    9. 10.8 mi/h
83. The variable a is an integer. Which of the following values could NOT equal a 3 ? eh cubed , question mark
    1. − 27 negative 27
    2. − 8 negative 8
    3. 16
    4. 64

Short Response

84. The leading scorer in your high school's soccer division finished the season with an average of 4 goals per game for 15 games. As the division's second-leading scorer, you have an average of 4 goals per game for 14 games. You still have to play your last game. How many goals must you score in the final game to overtake the division's leading scorer? Show your work.

Mixed Review

See Lesson 3-1.

Define a variable and write an inequality to model each situation.

85. A hummingbird migrates more than 1850 mi.
86. An octopus can be up to 18 ft long.

See Lesson 1-2.

Simplify.

87. 7 2 + 23 7 squared , plus 23
88. 3 ( 4 − 5 ) 2 − 4 3 . open 4 minus 5 close squared . minus 4
89. 0.4 + 0.2 ( 4.2 − 3.4 ) 0.4 plus 0.2 open 4.2 minus 3.4 close

Get Ready! To prepare for Lesson 3-3, do Exercises 90–92.

See Lesson 2-1.

Solve each equation.

90. 10 = v 2 10 equals , v over 2
91. 15 = − 22 y 15 equals negative 22 y
92. 3 4 z = − 18 3 fourths , z equals negative 18

Table of Contents