Question 1

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$4 x + 1 < 29$$

Accepted Answer

A)  $( * , 7 )$
 
B)  $( 7 , \infty )$
 
C)  $( * , 7 ]$
 
D)  $[ 7 , \infty )$

Question 2

Find the solution set for the equation.
-$$| 7 x + 6 | + 9 = 13$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 3 } , - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ \frac { 2 } { 7 } , \frac { 10 } { 7 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 2 } { 7 } , - \frac { 10 } { 7 } \right\}$

Question 3

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.
-$8\leq 2 x + 4 \leq 18$

Accepted Answer

A) $\text {  }(-\infty, 2) \cup(7, \infty)$
 
B) $\text {  }[2,7]$
 
C)  $( 2,7 )$
 
D)  $( - \infty , 2 ] \cup [ 7 , \infty )$

Question 4

Graph the inequality.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 5

Solve. Use interval notation to express the range.
-Parts for an automobile repair cost $609. The mechanic charges $29 per hour. If you receive an estimate for at least $783 and at most $870 for fixing the car, what is the time interval that the mechanic will be working on the job?

Accepted Answer

A)  [6, 9] 
B)  [1, 9] 
C)  [1, 6] 
D)  [27, 30]

Question 6

Find the solution set for the equation.
-$$| x - 9 | = 0$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\{ 9 \}$ 
C)  $\varnothing$ 
D)  $\{ - 9,9 \}$

Question 7

Solve. Use interval notation to express the range.
-On the first four exams, your grades are 79, 82, 75, and 80. There is still a final exam, and it counts as two grades. You are hoping to earn a C in the course. This will occur if the average of your six exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam will result in earning a C?

Accepted Answer

A)  [52, 82) 
B)  [52, 82] 
C)  [34, 84] 
D)  [34, 84)

Question 8

Solve and graph the solution set on a number line.
-$| x - 9 | + 3 \geq 11$

Accepted Answer

A)  $[ 1,17 ]$
 
B)  $( - \infty , 1 ) \cup ( 17 , \infty )$
 
C) $( - \infty , 1 ] \cup [ 17 , \infty )$

$\text { 
D)  } \phi$

Question 9

Solve.
-Using data from 2010-2012, the annual number of cars sold at a certain dealership can be modeled by the formula y = 4x + 3, where y is the number of cars, in thousands, sold x years after 2010. According to this formula, in which years will the number of cars sold exceed 31 thousand?

Accepted Answer

A)  Years after 2017 
B)  Years after 2019 
C)  Years after 2021 
D)  Years after 2015

Question 10

Solve and graph the solution set on a number line.
-$|x+3|-6 \leq-1$

Accepted Answer

A)  $( - 8,2 )$
 
B)  $[ - 8,2 ]$
 
C) $\text {  } \varnothing$ 
D)  [ - 8 , - 1 ]

Question 11

Graph the inequality.
-$$4 x + y \leq 2$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 12

Graph the inequality.
-$y>x+6$

Accepted Answer

A)

B) 
 
C) 
 
D)

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.
-$- 7 x > - 7$ and $x + 7 > 5$

Accepted Answer

A) $ ( 1 , \infty )$
 
B)  $( - 2,1 )$
 
C) $ ( - \infty , - 2 ) \cup ( 1 , \infty )$
 
D) $\phi$

Question 14

Solve.
-A standard train ticket in a certain city costs $1.50 per ride. People who use the train also have the option of purchasing a frequent-rider pass for $15.00 each month. With the pass, a ticket costs only $0.75 per ride. How many train rides in a month make the frequent-rider pass a better deal than standard train tickets?

Accepted Answer

A)  22 or more rides 
B)  19 or more rides 
C)  21 or more rides 
D)  20 or more rides

Question 15

Solve.
-Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90?

Accepted Answer

A)  93 or greater 
B)  95 or greater 
C)  94 or greater 
D)  96 or greater

Question 16

Graph the inequality.
-$$x + 2 y \geq 3$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 17

Solve and graph the solution set on a number line.
-$$| 3 ( x + 1 ) + 6 | \leq 9$$

Accepted Answer

A)  $( - 4,2 )$
 
B)  $( - 6,0 )$
 
C)  $[ - 6,0 ]$
 
D)  $[ - 4,2 ]$

Question 18

Find the solution set for the equation.
-$$| x - 8 | = | 9 - x |$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 17 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } \right\}$ 
D)  $\{ 17 \}$

Question 19

Graph the inequality.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 20

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$8 x - 10 \leq 2 x - 15$$

Accepted Answer

A)  $[ - 5,6 ]$
 
B)  $\left( - \infty , - \frac { 5 } { 6 } \right)$
 
C)  $( - 5,6 )$
 
D)  $\left[ - \infty , - \frac { 5 } { 6 } \right]$

Exam 4: Inequalities and Problem Solving

Solve the inequality. Other than Ø, graph the solution set on a number line. - $4 x + 1 < 29$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - 4 x + 1 < 29 A) ( * , 7 ) B) ( 7 , \infty ) C) ( * , 7 ] D) [ 7 , \infty )$

Find the solution set for the equation. - $| 7 x + 6 | + 9 = 13$

Graph the inequality. -

Solve. Use interval notation to express the range. -Parts for an automobile repair cost $609. The mechanic charges $29 per hour. If you receive an estimate for at least $783 and at most $870 for fixing the car, what is the time interval that the mechanic will be working on the job?

Find the solution set for the equation. - $| x - 9 | = 0$

Solve and graph the solution set on a number line. - $| x - 9 | + 3 \geq 11$ $Solve and graph the solution set on a number line. - | x - 9 | + 3 \geq 11 A) [ 1,17 ] B) ( - \infty , 1 ) \cup ( 17 , \infty ) C) ( - \infty , 1 ] \cup [ 17 , \infty ) \text { D) } \phi$

Solve. -Using data from 2010-2012, the annual number of cars sold at a certain dealership can be modeled by the formula y = 4x + 3, where y is the number of cars, in thousands, sold x years after 2010. According to this formula, in which years will the number of cars sold exceed 31 thousand?

Solve and graph the solution set on a number line. - $|x+3|-6 \leq-1$ $Solve and graph the solution set on a number line. - |x+3|-6 \leq-1 A) ( - 8,2 ) B) [ - 8,2 ] C) \text { } \varnothing D) [ - 8 , - 1 ]$

Graph the inequality. - $4 x + y \leq 2$ $Graph the inequality. - 4 x + y \leq 2 A) B) C) D)$

Graph the inequality. - $y>x+6$

Solve. -Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90?

Graph the inequality. - $x + 2 y \geq 3$ $Graph the inequality. - x + 2 y \geq 3 A) B) C) D)$

Solve and graph the solution set on a number line. - $| 3 ( x + 1 ) + 6 | \leq 9$ $Solve and graph the solution set on a number line. - | 3 ( x + 1 ) + 6 | \leq 9 A) ( - 4,2 ) B) ( - 6,0 ) C) [ - 6,0 ] D) [ - 4,2 ]$

Find the solution set for the equation. - $| x - 8 | = | 9 - x |$

Graph the inequality. -

Exam 4: Inequalities and Problem Solving

Solve the inequality. Other than Ø, graph the solution set on a number line. - 4x+1<294 x + 1 < 294x+1<29

Find the solution set for the equation. - ∣7x+6∣+9=13| 7 x + 6 | + 9 = 13∣7x+6∣+9=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. - 8≤2x+4≤188\leq 2 x + 4 \leq 188≤2x+4≤18

Graph the inequality. -

Solve. Use interval notation to express the range. -Parts for an automobile repair cost $609. The mechanic charges $29 per hour. If you receive an estimate for at least $783 and at most $870 for fixing the car, what is the time interval that the mechanic will be working on the job?

Find the solution set for the equation. - ∣x−9∣=0| x - 9 | = 0∣x−9∣=0

Solve and graph the solution set on a number line. - ∣x−9∣+3≥11| x - 9 | + 3 \geq 11∣x−9∣+3≥11

Solve. -Using data from 2010-2012, the annual number of cars sold at a certain dealership can be modeled by the formula y = 4x + 3, where y is the number of cars, in thousands, sold x years after 2010. According to this formula, in which years will the number of cars sold exceed 31 thousand?

Solve and graph the solution set on a number line. - ∣x+3∣−6≤−1|x+3|-6 \leq-1∣x+3∣−6≤−1

Graph the inequality. - 4x+y≤24 x + y \leq 24x+y≤2

Graph the inequality. - y>x+6y>x+6y>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. - −7x>−7- 7 x > - 7−7x>−7 and x+7>5x + 7 > 5x+7>5

Solve. -Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90?

Graph the inequality. - x+2y≥3x + 2 y \geq 3x+2y≥3

Solve and graph the solution set on a number line. - ∣3(x+1) +6∣≤9| 3 ( x + 1 ) + 6 | \leq 9∣3(x+1) +6∣≤9

Find the solution set for the equation. - ∣x−8∣=∣9−x∣| x - 8 | = | 9 - x |∣x−8∣=∣9−x∣

Graph the inequality. -

Solve the inequality. Other than Ø, graph the solution set on a number line. - 8x−10≤2x−158 x - 10 \leq 2 x - 158x−10≤2x−15

Solve the inequality. Other than Ø, graph the solution set on a number line. - $4 x + 1 < 29$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - 4 x + 1 < 29 A) ( * , 7 ) B) ( 7 , \infty ) C) ( * , 7 ] D) [ 7 , \infty )$

Find the solution set for the equation. - $| 7 x + 6 | + 9 = 13$

Find the solution set for the equation. - $| x - 9 | = 0$

Solve and graph the solution set on a number line. - $| x - 9 | + 3 \geq 11$ $Solve and graph the solution set on a number line. - | x - 9 | + 3 \geq 11 A) [ 1,17 ] B) ( - \infty , 1 ) \cup ( 17 , \infty ) C) ( - \infty , 1 ] \cup [ 17 , \infty ) \text { D) } \phi$

Solve and graph the solution set on a number line. - $|x+3|-6 \leq-1$ $Solve and graph the solution set on a number line. - |x+3|-6 \leq-1 A) ( - 8,2 ) B) [ - 8,2 ] C) \text { } \varnothing D) [ - 8 , - 1 ]$

Graph the inequality. - $4 x + y \leq 2$ $Graph the inequality. - 4 x + y \leq 2 A) B) C) D)$

Graph the inequality. - $y>x+6$

Graph the inequality. - $x + 2 y \geq 3$ $Graph the inequality. - x + 2 y \geq 3 A) B) C) D)$

Solve and graph the solution set on a number line. - $| 3 ( x + 1 ) + 6 | \leq 9$ $Solve and graph the solution set on a number line. - | 3 ( x + 1 ) + 6 | \leq 9 A) ( - 4,2 ) B) ( - 6,0 ) C) [ - 6,0 ] D) [ - 4,2 ]$

Find the solution set for the equation. - $| x - 8 | = | 9 - x |$