Question 1

Find the solution set for the equation.
-$$| 7 x - 7 | + 4 = 1$$

Accepted Answer

A)  $\left\{ \frac { 4 } { 7 } , - \frac { 10 } { 7 } \right\}$ 
B)  $\left\{ \frac { 10 } { 7 } , - \frac { 4 } { 7 } \right\}$ 
C)  $\left\{ \frac { 4 } { 7 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 4 } { 7 } , - \frac { 10 } { 7 } \right\}$ 
B)  $\left\{ \frac { 10 } { 7 } , - \frac { 4 } { 7 } \right\}$ 
C)  $\left\{ \frac { 4 } { 7 } \right\}$ 
D)  $\varnothing$

Question 2

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.
-$20 < 5 x \leq 25$

Accepted Answer

A)  $( - \infty , 4 ] \cup ( 5 , \infty )$
  
B)  $[ 4,5 )$
  
C)  $( 4,5 ]$
  
D) $( - \infty , 4 ) \cup [ 5 , \infty )$
  
A)  $( - \infty , 4 ] \cup ( 5 , \infty )$
  
B)  $[ 4,5 )$
  
C)  $( 4,5 ]$
  
D) $( - \infty , 4 ) \cup [ 5 , \infty )$

Question 3

Find the solution set for the equation.
-$$| 3 x + 2 | = | 3 x - 2 |$$

Accepted Answer

A)  $\{ 0,3 \}$ 
B)  $\{ 0,2 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$ 
A)  $\{ 0,3 \}$ 
B)  $\{ 0,2 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$

Question 4

Find the union of the sets.
-$\{ w , h , a , t , s \} \cup \varnothing$

Accepted Answer

A)  $\{ a , s \}$ 
B)  $\{ w \}$ 
C)  $\varnothing$ 
D)  $\{ w , h , a , t , s \}$ 
A)  $\{ a , s \}$ 
B)  $\{ w \}$ 
C)  $\varnothing$ 
D)  $\{ w , h , a , t , s \}$

Question 5

Find the intersection of the sets.
-$$\{ - 5 , - 1,2,6 \} \cap \{ - 4,1,5,8 \}$$

Accepted Answer

A)  $\{ 1 \}$ 
B)  $\{ - 5 , - 4 , - 1,1,2,5,6,8 \}$ 
C)  $\varnothing$ 
D)  $\{ - 1,1,2 \}$ 
A)  $\{ 1 \}$ 
B)  $\{ - 5 , - 4 , - 1,1,2,5,6,8 \}$ 
C)  $\varnothing$ 
D)  $\{ - 1,1,2 \}$

Question 6

Solve and graph the solution set on a number line.
-$|x|<8$

Accepted Answer

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

Question 7

Solve and graph the solution set on a number line.
-$| x + 9 | > 0$

Accepted Answer

A)  $( - 9 , \infty )$
  
B)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$
  
C) $\text {  } \phi$ 
D)  $( - 9,9 )$
  
A)  $( - 9 , \infty )$
  
B)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$
  
C) $\text {  } \phi$ 
D)  $( - 9,9 )$

Question 8

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$- 2 ( 2 x - 8 ) < - 6 x + 2$

Accepted Answer

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

Question 9

Graph the inequality.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

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.
-$-4 x5$

Accepted Answer

A)  $( 1,3 )$
  
B)  $\varnothing$ 
C) $( 3 , \infty )$
  
D)  $( - \infty , 1 ) \cup ( 3 , \infty )$
  
A)  $( 1,3 )$
  
B)  $\varnothing$ 
C) $( 3 , \infty )$
  
D)  $( - \infty , 1 ) \cup ( 3 , \infty )$

Question 11

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.
-$\mathrm { X } > 4 \mathrm { Or } x < 4$

Accepted Answer

A)  $( - \infty , 4 )$
  
B)  $\left( \frac { 4 } { 4 } ( x ) \right)$
  
C) 
$\phi$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$
  
A)  $( - \infty , 4 )$
  
B)  $\left( \frac { 4 } { 4 } ( x ) \right)$
  
C) 
$\phi$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 12

Solve and graph the solution set on a number line.
-$| x + 8 | \leq 0$

Accepted Answer

A)  $( - \infty , - 8 )$
  
B) $\{ 8 \}$
  
C) 
$\varnothing$ 
D)  $\{ - 8 \}$
  
A)  $( - \infty , - 8 )$
  
B) $\{ 8 \}$
  
C) 
$\varnothing$ 
D)  $\{ - 8 \}$

Question 13

Solve and graph the solution set on a number line.
-$| x + 7 | < 6$

Accepted Answer

A)  $Q$ 
B)  $( - 13 , - 1 )$
  
C) $[ - 13 , - 1 ]$
  
D)  $( - \infty , - 13 ) \cup ( - 1 , \infty )$
  
A)  $Q$ 
B)  $( - 13 , - 1 )$
  
C) $[ - 13 , - 1 ]$
  
D)  $( - \infty , - 13 ) \cup ( - 1 , \infty )$

Question 14

Graph the inequality.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$4 x - 3 \geq 3 x - 9$

Accepted Answer

A) $ [ - 6 , \infty )$
  
B)  $( - \infty , - 6 )$
  
C) $( - 6 , \infty )$
  
D)  $( - \infty , - 6 ]$
  
A) $ [ - 6 , \infty )$
  
B)  $( - \infty , - 6 )$
  
C) $( - 6 , \infty )$
  
D)  $( - \infty , - 6 ]$

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.
-$x \leq 3$ and $x \leq 1$

Accepted Answer

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

Question 17

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
-$| 5 x - 4 | - 6 > - 9$

Accepted Answer

A)  $\varnothing$
  
B)  $\left( \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$
  
C)  $\left( \frac { 1 } { 5 } , \infty \right)$
  
D)  $( - \infty , \infty )$
  
A)  $\varnothing$
  
B)  $\left( \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$
  
C)  $\left( \frac { 1 } { 5 } , \infty \right)$
  
D)  $( - \infty , \infty )$

Question 18

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$14 x - 18 > 2 ( 6 x - 4 )$

Accepted Answer

A)  $[ 5 , \infty )$
  
B) $( \infty , 5 )$
  
C) $\text {  }(*, 5]$
  
D) $\text {  }(5, \infty)$
  
A)  $[ 5 , \infty )$
  
B) $( \infty , 5 )$
  
C) $\text {  }(*, 5]$
  
D) $\text {  }(5, \infty)$

Question 19

Solve.
-It takes 22 minutes to set up a candy making machine. Once the machine is set up, it produces 10 candies per minute. Use an inequality to find the number of candies that can be produced in 2 hours if the machine has not yet been set up.

Accepted Answer

A)  980 candies or fewer 
B)  20 candies or fewer 
C)  440 candies or fewer 
D)  2420 candies or fewer 
A)  980 candies or fewer 
B)  20 candies or fewer 
C)  440 candies or fewer 
D)  2420 candies or fewer

Question 20

Solve.
-ABC phone company charges $21 per month plus 8¢ per minute of phone calls. XYZ phone company charges $15 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month make XYZ phone company the better deal?

Accepted Answer

A)  More than 30 minutes 
B)  Less than 300 minutes 
C)  Less than 30 minutes 
D)  More than 300 minutes 
A)  More than 30 minutes 
B)  Less than 300 minutes 
C)  Less than 30 minutes 
D)  More than 300 minutes

Find the solution set for the equation. - $| 7 x - 7 | + 4 = 1$

Find the solution set for the equation. - $| 3 x + 2 | = | 3 x - 2 |$

Find the union of the sets. - $\{ w , h , a , t , s \} \cup \varnothing$

Find the intersection of the sets. - $\{ - 5 , - 1,2,6 \} \cap \{ - 4,1,5,8 \}$

Solve and graph the solution set on a number line. - $|x|<8$

Solve and graph the solution set on a number line. - $| x + 9 | > 0$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 2 ( 2 x - 8 ) < - 6 x + 2$

Graph the inequality. -

Solve and graph the solution set on a number line. - $| x + 8 | \leq 0$ $Solve and graph the solution set on a number line. - | x + 8 | \leq 0$

Solve and graph the solution set on a number line. - $| x + 7 | < 6$

Graph the inequality. -

Solve the inequality. Other than Ø, graph the solution set on a number line. - $4 x - 3 \geq 3 x - 9$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - 4 x - 3 \geq 3 x - 9$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| 5 x - 4 | - 6 > - 9$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $14 x - 18 > 2 ( 6 x - 4 )$

Solve. -It takes 22 minutes to set up a candy making machine. Once the machine is set up, it produces 10 candies per minute. Use an inequality to find the number of candies that can be produced in 2 hours if the machine has not yet been set up.

Solve. -ABC phone company charges $21 per month plus 8¢ per minute of phone calls. XYZ phone company charges $15 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month make XYZ phone company the better deal?

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Polynomials, Polynomial Functions, and Factoring

Rational Expressions, Functions, and Equations

Radicals, Radical Functions, and Rational Exponents

Quadratic Equations and Functions

Filters

Exam 4: Inequalities and Problem Solving

Find the solution set for the equation. - ∣7x−7∣+4=1| 7 x - 7 | + 4 = 1∣7x−7∣+4=1

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. - 20<5x≤2520 < 5 x \leq 2520<5x≤25

Find the solution set for the equation. - ∣3x+2∣=∣3x−2∣| 3 x + 2 | = | 3 x - 2 |∣3x+2∣=∣3x−2∣

Find the union of the sets. - {w,h,a,t,s}∪∅\{ w , h , a , t , s \} \cup \varnothing{w,h,a,t,s}∪∅

Find the intersection of the sets. - {−5,−1,2,6}∩{−4,1,5,8}\{ - 5 , - 1,2,6 \} \cap \{ - 4,1,5,8 \}{−5,−1,2,6}∩{−4,1,5,8}

Solve and graph the solution set on a number line. - ∣x∣<8|x|<8∣x∣<8

Solve and graph the solution set on a number line. - ∣x+9∣>0| x + 9 | > 0∣x+9∣>0

Solve the inequality. Other than Ø, graph the solution set on a number line. - −2(2x−8)<−6x+2- 2 ( 2 x - 8 ) < - 6 x + 2−2(2x−8)<−6x+2

Graph the inequality. -

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 and x+4>5-4 x<-12 \text { and } x+4>5−4x<−12 and x+4>5

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. - X>4Orx<4\mathrm { X } > 4 \mathrm { Or } x < 4X>4Orx<4

Solve and graph the solution set on a number line. - ∣x+8∣≤0| x + 8 | \leq 0∣x+8∣≤0

Solve and graph the solution set on a number line. - ∣x+7∣<6| x + 7 | < 6∣x+7∣<6

Graph the inequality. -

Solve the inequality. Other than Ø, graph the solution set on a number line. - 4x−3≥3x−94 x - 3 \geq 3 x - 94x−3≥3x−9

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. - x≤3x \leq 3x≤3 and x≤1x \leq 1x≤1

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - ∣5x−4∣−6>−9| 5 x - 4 | - 6 > - 9∣5x−4∣−6>−9

Solve the inequality. Other than Ø, graph the solution set on a number line. - 14x−18>2(6x−4)14 x - 18 > 2 ( 6 x - 4 )14x−18>2(6x−4)

Solve. -It takes 22 minutes to set up a candy making machine. Once the machine is set up, it produces 10 candies per minute. Use an inequality to find the number of candies that can be produced in 2 hours if the machine has not yet been set up.

Solve. -ABC phone company charges $21 per month plus 8¢ per minute of phone calls. XYZ phone company charges $15 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month make XYZ phone company the better deal?

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Polynomials, Polynomial Functions, and Factoring

Rational Expressions, Functions, and Equations

Radicals, Radical Functions, and Rational Exponents

Quadratic Equations and Functions

Filters

Find the solution set for the equation. - $| 7 x - 7 | + 4 = 1$

Find the solution set for the equation. - $| 3 x + 2 | = | 3 x - 2 |$

Find the union of the sets. - $\{ w , h , a , t , s \} \cup \varnothing$

Find the intersection of the sets. - $\{ - 5 , - 1,2,6 \} \cap \{ - 4,1,5,8 \}$

Solve and graph the solution set on a number line. - $|x|<8$

Solve and graph the solution set on a number line. - $| x + 9 | > 0$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 2 ( 2 x - 8 ) < - 6 x + 2$

Solve and graph the solution set on a number line. - $| x + 8 | \leq 0$ $Solve and graph the solution set on a number line. - | x + 8 | \leq 0$

Solve and graph the solution set on a number line. - $| x + 7 | < 6$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $4 x - 3 \geq 3 x - 9$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - 4 x - 3 \geq 3 x - 9$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| 5 x - 4 | - 6 > - 9$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $14 x - 18 > 2 ( 6 x - 4 )$