Question 1

Solve.
-When making a long distance call from a certain pay phone, the first three minutes of a call cost $1.15. After that, each additional minute or portion of a minute of that call costs $0.20. Use an inequality to find the number of minutes one can call long distance for $2.15.

Accepted Answer

A)  5 minutes or fewer 
B)  11 minutes or fewer 
C)  2 minutes or fewer 
D)  8 minutes or fewer

Question 2

Solve.
-When a number is subtracted from -7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition.

Accepted Answer

A)  $( \infty , - 4 ) \cup ( 10 , \infty )$ 
B)  $( \infty , - 10 ) \cup ( - 4 , \infty )$ 
C)  $( \infty , - 10 ] \cup [ - 4 , \infty )$ 
D)  $( - 10 , - 4 )$

Question 3

Find the solution set for the equation.
-$$| 4 x + 9 | = | x - 4 |$$

Accepted Answer

A)  $\left\{ \frac { 13 } { 3 } , 1 \right\}$ 
B)  $\left\{ - \frac { 13 } { 3 } , \frac { 22 } { 5 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 13 } { 3 } , - 1 \right\}$

Question 4

Solve. Use interval notation to express the range.
-The formula for converting Celsius temperature, $C$, to Fahrenheit temperature, $F$, is
$$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text {. }$$
If Fahrenheit temperature ranges from $41 ^ { \circ }$ to $176 ^ { \circ }$, inclusive, what is the range for the Celsius temperature?

Accepted Answer

A)  $( 5,80 )$ 
B)  $[ 106,349 ]$ 
C)  $[ 5,80 ]$ 
D)  $( 106,349 )$

Question 5

Find the solution set for the equation.
-$$| x | = 6$$

Accepted Answer

A)  $\{ 36 \}$ 
B)  $\{ - 6 \}$ 
C)  $\{ - 6,6 \}$ 
D)  $\{ 6 \}$

Question 6

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$- 4 x + 1 \geq 9$ or $6 x + 3 \geq - 21$

Accepted Answer

A)  $( - \infty , \infty )$
 
B)  $[ - 4 , \infty )$
 
C) $[ - 4 , - 2 ]$
 
D)  $[ - 2 , \infty )$

Question 7

Graph the inequality.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 8

Solve. Use interval notation to express the range.
-The formula C = 0.5x + 18 represents the estimated future cost of yearly attendance at State University, where C is the cost in thousands of dollars x years after 2010. Use a compound inequality to determine in which years attendance costs will range from 22 to 24 thousand dollars.

Accepted Answer

A)  [2017, 2021] 
B)  [2018, 2022] 
C)  [2019, 2023] 
D)  [2019, 2021]

Question 9

Find the solution set for the equation.
-$\left| \frac { 2 x + 5 } { 3 } \right| = 3$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\{ 7 \}$ 
C)  $\{ 2 , - 7 \rangle$ 
D)  $\varnothing$

Question 10

Graph the inequality.
-$$\frac { x } { 5 } + \frac { y } { 3 } \leq 1$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

Solve.
-Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

Accepted Answer

A)  $| h - b | > 0.2$ 
B)  $| b + h | \geq 0.2$ 
C)  $| b - h | \leq 0.2$ 
D)  $| b - h | < 0.2$

Question 12

Solve.
-Greg is opening a car wash. He estimates his cost equation as C = 8000 + 0.08x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.

Accepted Answer

A)  At least 45,198 cars 
B)  At least 4520 cars 
C)  At least 3520 cars 
D)  At least 452 cars

Question 13

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$$17 \leq \frac { 9 x } { 7 } + 8 < 26$$

Accepted Answer

A)  $( 7,14 ]$
 
B)  $( 7,8 ]$
 
C)  $[ 7,14 )$
 
D)  $[ 7,8 )$

Question 14

Solve.
-The radius r of a plastic tube used in manufacturing a child's toy must not differ from the standard s by more than 5 millimeters. The manufacturing engineers express this as |r - s| ≤5. If the standard s is 33, solve the inequality for the radius r. Express the answer in set-builder notation.

Accepted Answer

A)  $\{ \mathrm { r } \mid 23 \leq \mathrm { r } \leq 28 \}$ 
B)  $\{ \mathrm { r } \mid 28 \leq \mathrm { r } \leq 38 \}$ 
C)  $\{ \mathrm { r } \mid \mathrm { r } \leq 28$ or $\mathrm { r } \geq 38 \}$ 
D)  $\{ \mathrm { r } \mid \mathrm { r } \leq 23$ or $\mathrm { r } \geq 28 \}$

Question 15

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$-31 \leq-4 x-3<-15$

Accepted Answer

A)  $\varnothing$ 
B)  $[ 3,7 )$
 
C)  $( 3,7 ]$
 
D)  $( - \infty , 3 ] \cup ( 7 , \infty )$

Question 16

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$- 4 x \leq - 12$ or $4 x > 12 x - 8$

Accepted Answer

A) $\text {  }(-\infty, 1] \cup(3, \infty)$
 
B)  $( - \infty , 1 ) \cup [ 3 , \infty )$
 
C) $\varnothing$ 
D)  $( 1,3 ]$

Question 17

Find the intersection of the sets.
-$\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}$

Accepted Answer

A)  $\{ 2,5,8 \}$ 
B)  $\{ - 4,0,2,5,8 \}$ 
C)  $\{ - 4,0,2,5 \}$ 
D)  $\{ 2,5 \}$

Question 18

Graph the inequality.
-$$y \geq - \frac { 1 } { 2 } x$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 19

Solve and graph the solution set on a number line.
-$$5 + \left| 1 - \frac { x } { 2 } \right| \geq 8$$

Accepted Answer

A)  $[ - 8,4 ]$
 
B)  $( - \infty , - 8 ] \cup [ 4 , \infty )$
 
C)  $( - \infty , - 4 ] \cup [ 8 , \infty )$
 
D)  $[ - 4,8 ]$

Question 20

Solve and graph the solution set on a number line.
-$$2 + \left| 1 - \frac { x } { 2 } \right| \leq 5$$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ 8 , \infty )$
 
B)  $[ - 4,8 ]$
 
C)  $( - \infty , - 8 ] \cup [ 4 , \infty )$
 
D)  $[ - 8,4 ]$

Exam 4: Inequalities and Problem Solving

Solve. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $1.15. After that, each additional minute or portion of a minute of that call costs $0.20. Use an inequality to find the number of minutes one can call long distance for $2.15.

Solve. -When a number is subtracted from -7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition.

Find the solution set for the equation. - $| 4 x + 9 | = | x - 4 |$

Find the solution set for the equation. - $| x | = 6$

Graph the inequality. -

Find the solution set for the equation. - $\left| \frac { 2 x + 5 } { 3 } \right| = 3$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 3 } \leq 1 A) B) C) D)$

Solve. -Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

Solve. -Greg is opening a car wash. He estimates his cost equation as C = 8000 + 0.08x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $-31 \leq-4 x-3<-15$

Find the intersection of the sets. - $\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}$

Graph the inequality. - $y \geq - \frac { 1 } { 2 } x$ $Graph the inequality. - y \geq - \frac { 1 } { 2 } x A) B) C) D)$

Exam 4: Inequalities and Problem Solving

Solve. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $1.15. After that, each additional minute or portion of a minute of that call costs $0.20. Use an inequality to find the number of minutes one can call long distance for $2.15.

Solve. -When a number is subtracted from -7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition.

Find the solution set for the equation. - ∣4x+9∣=∣x−4∣| 4 x + 9 | = | x - 4 |∣4x+9∣=∣x−4∣

Find the solution set for the equation. - ∣x∣=6| x | = 6∣x∣=6

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - −4x+1≥9- 4 x + 1 \geq 9−4x+1≥9 or 6x+3≥−216 x + 3 \geq - 216x+3≥−21

Graph the inequality. -

Find the solution set for the equation. - ∣2x+53∣=3\left| \frac { 2 x + 5 } { 3 } \right| = 3​32x+5​​=3

Graph the inequality. - x5+y3≤1\frac { x } { 5 } + \frac { y } { 3 } \leq 15x​+3y​≤1

Solve. -Chi is assigned to construct a triangle with the measure b of the base and the measure h of the height differing by no more than 0.2 centimeters. Express the relationship between b and h as an inequality involving absolute value.

Solve. -Greg is opening a car wash. He estimates his cost equation as C = 8000 + 0.08x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - 17≤9x7+8<2617 \leq \frac { 9 x } { 7 } + 8 < 2617≤79x​+8<26

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - −31≤−4x−3<−15-31 \leq-4 x-3<-15−31≤−4x−3<−15

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - −4x≤−12- 4 x \leq - 12−4x≤−12 or 4x>12x−84 x > 12 x - 84x>12x−8

Find the intersection of the sets. - {−4,0,2,5}∩{2,5,8}\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}{−4,0,2,5}∩{2,5,8}

Graph the inequality. - y≥−12xy \geq - \frac { 1 } { 2 } xy≥−21​x

Solve and graph the solution set on a number line. - 5+∣1−x2∣≥85 + \left| 1 - \frac { x } { 2 } \right| \geq 85+​1−2x​​≥8

Solve and graph the solution set on a number line. - 2+∣1−x2∣≤52 + \left| 1 - \frac { x } { 2 } \right| \leq 52+​1−2x​​≤5

Find the solution set for the equation. - $| 4 x + 9 | = | x - 4 |$

Find the solution set for the equation. - $| x | = 6$

Find the solution set for the equation. - $\left| \frac { 2 x + 5 } { 3 } \right| = 3$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 3 } \leq 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 3 } \leq 1 A) B) C) D)$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $-31 \leq-4 x-3<-15$

Find the intersection of the sets. - $\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}$

Graph the inequality. - $y \geq - \frac { 1 } { 2 } x$ $Graph the inequality. - y \geq - \frac { 1 } { 2 } x A) B) C) D)$