Question 1

Solve the compound inequality. Graph the solution set.
-$x \leq 5$ and $x \leq - 3$

Accepted Answer

A)  $( - \infty , - 3 ]$
  
B)  $[ - 3,5 ]$
  
C) $[ - 3 , \infty )$
  
D)  $( - \infty , - 3 ] \cup [ 5 , \infty )$
  
A)  $( - \infty , - 3 ]$
  
B)  $[ - 3,5 ]$
  
C) $[ - 3 , \infty )$
  
D)  $( - \infty , - 3 ] \cup [ 5 , \infty )$

Question 2

Solve the inequality. Graph the solution set.
-$| 4 x - 3 | > 0$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$
  
B)  $\left( \frac { 3 } { 4 } , \infty \right)$
  
C)  $\left( - \infty , \frac { 3 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$
  
D)  $\left( - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right)$
  
A)  $\left( - \infty , - \frac { 3 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$
  
B)  $\left( \frac { 3 } { 4 } , \infty \right)$
  
C)  $\left( - \infty , \frac { 3 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$
  
D)  $\left( - \frac { 3 } { 4 } , \frac { 3 } { 4 } \right)$

Question 3

Solve the inequality. Graph the solution set.
-$| 8 k + 9 | < - 8$

Accepted Answer

A)  $\left( - \frac { 17 } { 8 } , - \frac { 1 } { 8 } \right)$
  
B)  $\left( - \infty , - \frac { 17 } { 8 } \right) \cup \left( - \frac { 1 } { 8 } , \infty \right)$
  
C)  $\left( \frac { 1 } { 8 } , \frac { 17 } { 8 } \right)$
  
D)  $\varnothing$
  
A)  $\left( - \frac { 17 } { 8 } , - \frac { 1 } { 8 } \right)$
  
B)  $\left( - \infty , - \frac { 17 } { 8 } \right) \cup \left( - \frac { 1 } { 8 } , \infty \right)$
  
C)  $\left( \frac { 1 } { 8 } , \frac { 17 } { 8 } \right)$
  
D)  $\varnothing$

Question 4

Solve the absolute value equation.
-$| x | = 3$

Accepted Answer

A)  3 
B)  $- 3$ 
C)  9 
D)  $3 , - 3$ 
A)  3 
B)  $- 3$ 
C)  9 
D)  $3 , - 3$

Question 5

Fill in the blank with one of the words or phrases listed below.

compound inequality &emsp; solution&emsp;  system of linear inequalities &emsp; 
absolute value &emsp; union &emsp; intersection

-Two or more linear inequalities are called a(n) .

Accepted Answer

A)  system of linear inequalities 
B)  absolute value 
C)  intersection 
D)  solution 
A)  system of linear inequalities 
B)  absolute value 
C)  intersection 
D)  solution

Question 6

Solve the equation or inequality.
-$| 3 x + 6 | \geq 2$

Accepted Answer

A)  $\left[ - \frac { 4 } { 3 } , \infty \right]$ 
B)  $\left[ - \frac { 8 } { 3 } , - \frac { 4 } { 3 } \right]$ 
C)  $\left( - \frac { 8 } { 3 } , - \frac { 4 } { 3 } \right)$ 
D)  $\left( - \infty , - \frac { 8 } { 3 } \right] \cup \left[ - \frac { 4 } { 3 } , \infty \right)$ 
A)  $\left[ - \frac { 4 } { 3 } , \infty \right]$ 
B)  $\left[ - \frac { 8 } { 3 } , - \frac { 4 } { 3 } \right]$ 
C)  $\left( - \frac { 8 } { 3 } , - \frac { 4 } { 3 } \right)$ 
D)  $\left( - \infty , - \frac { 8 } { 3 } \right] \cup \left[ - \frac { 4 } { 3 } , \infty \right)$

Question 7

Determine whether the ordered pair given is a solution of the linear inequality in two variables.
-$2 x + 3 y \leq 3 ; ( 3,4 )$

Accepted Answer

A) True 
 B)False

Question 8

Graph the inequality.
-$4 x-2 y \leq-12$

Accepted Answer

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

Question 9

Solve the inequality. Graph the solution set.
-$|2 k-7| \leq 8$

Accepted Answer

A) $\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{15}{2}, \infty\right)$
  
B) $\left(-\frac{1}{2}, \frac{15}{2}\right)$
  
C) $\left(-\infty, \frac{15}{2}\right]$
  
D) $\left[-\frac{1}{2}, \frac{15}{2}\right]$
  
A) $\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{15}{2}, \infty\right)$
  
B) $\left(-\frac{1}{2}, \frac{15}{2}\right)$
  
C) $\left(-\infty, \frac{15}{2}\right]$
  
D) $\left[-\frac{1}{2}, \frac{15}{2}\right]$

Question 10

Graph the inequality.
-$2 x+5 y \leq 10$

Accepted Answer

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

Question 11

Write the inequality.
-Write an absolute value inequality representing all numbers x whose distance from 0 is greater than 4 units.

Accepted Answer

A)  $| x | \geq 4$ 
B)  $| x | \geq 5$ 
C)  $| x |  4$ 
A)  $| x | \geq 4$ 
B)  $| x | \geq 5$ 
C)  $| x |  4$

Question 12

Fill in the blank with one of the words or phrases listed below.

compound inequality &emsp; solution&emsp;  system of linear inequalities &emsp; 
absolute value &emsp; union &emsp; intersection

-The of two sets in the set of all elements that belong to either of the sets.

Accepted Answer

A)  intersection 
B)  solution 
C)  union 
D)  absolute value 
A)  intersection 
B)  solution 
C)  union 
D)  absolute value

Question 13

Solve the equation or inequality.
-$x \geq 4$ and $x \geq - 1$

Accepted Answer

A)  $\varnothing$ 
B)  $[ - 1,4 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $[ 4 , \infty )$ 
A)  $\varnothing$ 
B)  $[ - 1,4 ]$ 
C)  $[ - 1 , \infty )$ 
D)  $[ 4 , \infty )$

Question 14

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

Accepted Answer

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

Question 15

Solve the equation or inequality.
-$x \geq 2$ or $x \geq - 2$

Accepted Answer

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

Question 16

Solve the equation or inequality.
-$| x - 3 | = | 8 - x |$

Accepted Answer

A)  $\frac { 11 } { 2 }$ 
B)  11 
C)  $\varnothing$ 
D)  $- \frac { 2 } { 11 }$ 
A)  $\frac { 11 } { 2 }$ 
B)  11 
C)  $\varnothing$ 
D)  $- \frac { 2 } { 11 }$

Question 17

Solve the absolute value equation.
-$| 6 x + 2 | + 2 = 8$

Accepted Answer

A)  $\varnothing$ 
B)  $2 , - 4$ 
C)  $- \frac { 2 } { 3 } , \frac { 4 } { 3 }$ 
D)  $\frac { 2 } { 3 } , - \frac { 4 } { 3 }$ 
A)  $\varnothing$ 
B)  $2 , - 4$ 
C)  $- \frac { 2 } { 3 } , \frac { 4 } { 3 }$ 
D)  $\frac { 2 } { 3 } , - \frac { 4 } { 3 }$

Question 18

Solve the absolute value equation.
-$| 17 x | = 57.8$

Accepted Answer

A)  3.4, -3.4 
B)  -3.4 
C)  0, 3.4, -3.4 
D)  3.4 
A)  3.4, -3.4 
B)  -3.4 
C)  0, 3.4, -3.4 
D)  3.4

Question 19

List the elements of the set.
-If $A = \{ 19,21,22,23,26 \}$ and $B = \{ 19,21,22,23 \}$, list the elements of $A \cup B$.

Accepted Answer

A)  $\{ 26 \}$ 
B)  $\{ 19,21,22,23 \}$ 
C) {   } 
D)  $\{ 19,21,22,23,26 \}$ 
A)  $\{ 26 \}$ 
B)  $\{ 19,21,22,23 \}$ 
C) {   } 
D)  $\{ 19,21,22,23,26 \}$

Question 20

List the elements of the set.
-If $A = \{ x \mid x$ is an odd integer $\}$ and $B = \{ x \mid x$ is an even integer $\}$, list the elements of $A \cup B$.

Accepted Answer

A)  $\{ x \mid x$ is an integer $\}$ 
B)  $\{ x \mid x$ is an even integer $\}$ 
C)  $\{ 0 \}$ 
D)  {  } 
A)  $\{ x \mid x$ is an integer $\}$ 
B)  $\{ x \mid x$ is an even integer $\}$ 
C)  $\{ 0 \}$ 
D)  {  }

Solve the compound inequality. Graph the solution set. - $x \leq 5$ and $x \leq - 3$ $Solve the compound inequality. Graph the solution set. - x \leq 5 and x \leq - 3$

Solve the inequality. Graph the solution set. - $| 4 x - 3 | > 0$

Solve the inequality. Graph the solution set. - $| 8 k + 9 | < - 8$

Solve the absolute value equation. - $| x | = 3$

Fill in the blank with one of the words or phrases listed below. compound inequality solution system of linear inequalities absolute value union intersection -Two or more linear inequalities are called a(n) .

Solve the equation or inequality. - $| 3 x + 6 | \geq 2$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $2 x + 3 y \leq 3 ; ( 3,4 )$

Graph the inequality. - $4 x-2 y \leq-12$ $Graph the inequality. - 4 x-2 y \leq-12$

Solve the inequality. Graph the solution set. - $|2 k-7| \leq 8$ $Solve the inequality. Graph the solution set. - |2 k-7| \leq 8$

Graph the inequality. - $2 x+5 y \leq 10$ $Graph the inequality. - 2 x+5 y \leq 10$

Write the inequality. -Write an absolute value inequality representing all numbers x whose distance from 0 is greater than 4 units.

Fill in the blank with one of the words or phrases listed below. compound inequality solution system of linear inequalities absolute value union intersection -The of two sets in the set of all elements that belong to either of the sets.

Solve the equation or inequality. - $x \geq 4$ and $x \geq - 1$

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

Solve the equation or inequality. - $x \geq 2$ or $x \geq - 2$

Solve the equation or inequality. - $| x - 3 | = | 8 - x |$

Solve the absolute value equation. - $| 6 x + 2 | + 2 = 8$

Solve the absolute value equation. - $| 17 x | = 57.8$

List the elements of the set. -If $A = \{ 19,21,22,23,26 \}$ and $B = \{ 19,21,22,23 \}$ , list the elements of $A \cup B$ .

List the elements of the set. -If $A = \{ x \mid x$ is an odd integer $\}$ and $B = \{ x \mid x$ is an even integer $\}$ , list the elements of $A \cup B$ .

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Inequalities and Absolute Value

Solve the compound inequality. Graph the solution set. - x≤5x \leq 5x≤5 and x≤−3x \leq - 3x≤−3

Solve the inequality. Graph the solution set. - ∣4x−3∣>0| 4 x - 3 | > 0∣4x−3∣>0

Solve the inequality. Graph the solution set. - ∣8k+9∣<−8| 8 k + 9 | < - 8∣8k+9∣<−8

Solve the absolute value equation. - ∣x∣=3| x | = 3∣x∣=3

Fill in the blank with one of the words or phrases listed below. compound inequality solution system of linear inequalities absolute value union intersection -Two or more linear inequalities are called a(n) .

Solve the equation or inequality. - ∣3x+6∣≥2| 3 x + 6 | \geq 2∣3x+6∣≥2

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - 2x+3y≤3;(3,4)2 x + 3 y \leq 3 ; ( 3,4 )2x+3y≤3;(3,4)

Graph the inequality. - 4x−2y≤−124 x-2 y \leq-124x−2y≤−12

Solve the inequality. Graph the solution set. - ∣2k−7∣≤8|2 k-7| \leq 8∣2k−7∣≤8

Graph the inequality. - 2x+5y≤102 x+5 y \leq 102x+5y≤10

Write the inequality. -Write an absolute value inequality representing all numbers x whose distance from 0 is greater than 4 units.

Fill in the blank with one of the words or phrases listed below. compound inequality solution system of linear inequalities absolute value union intersection -The of two sets in the set of all elements that belong to either of the sets.

Solve the equation or inequality. - x≥4x \geq 4x≥4 and x≥−1x \geq - 1x≥−1

Graph the inequality. - x+2y≤3x+2 y \leq 3x+2y≤3

Solve the equation or inequality. - x≥2x \geq 2x≥2 or x≥−2x \geq - 2x≥−2

Solve the equation or inequality. - ∣x−3∣=∣8−x∣| x - 3 | = | 8 - x |∣x−3∣=∣8−x∣

Solve the absolute value equation. - ∣6x+2∣+2=8| 6 x + 2 | + 2 = 8∣6x+2∣+2=8

Solve the absolute value equation. - ∣17x∣=57.8| 17 x | = 57.8∣17x∣=57.8

List the elements of the set. -If A={19,21,22,23,26}A = \{ 19,21,22,23,26 \}A={19,21,22,23,26} and B={19,21,22,23}B = \{ 19,21,22,23 \}B={19,21,22,23} , list the elements of A∪BA \cup BA∪B .

List the elements of the set. -If A={x∣xA = \{ x \mid xA={x∣x is an odd integer }\}} and B={x∣xB = \{ x \mid xB={x∣x is an even integer }\}} , list the elements of A∪BA \cup BA∪B .

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve the compound inequality. Graph the solution set. - $x \leq 5$ and $x \leq - 3$ $Solve the compound inequality. Graph the solution set. - x \leq 5 and x \leq - 3$

Solve the inequality. Graph the solution set. - $| 4 x - 3 | > 0$

Solve the inequality. Graph the solution set. - $| 8 k + 9 | < - 8$

Solve the absolute value equation. - $| x | = 3$

Solve the equation or inequality. - $| 3 x + 6 | \geq 2$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $2 x + 3 y \leq 3 ; ( 3,4 )$

Graph the inequality. - $4 x-2 y \leq-12$ $Graph the inequality. - 4 x-2 y \leq-12$

Solve the inequality. Graph the solution set. - $|2 k-7| \leq 8$ $Solve the inequality. Graph the solution set. - |2 k-7| \leq 8$

Graph the inequality. - $2 x+5 y \leq 10$ $Graph the inequality. - 2 x+5 y \leq 10$

Solve the equation or inequality. - $x \geq 4$ and $x \geq - 1$

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

Solve the equation or inequality. - $x \geq 2$ or $x \geq - 2$

Solve the equation or inequality. - $| x - 3 | = | 8 - x |$

Solve the absolute value equation. - $| 6 x + 2 | + 2 = 8$

Solve the absolute value equation. - $| 17 x | = 57.8$

List the elements of the set. -If $A = \{ 19,21,22,23,26 \}$ and $B = \{ 19,21,22,23 \}$ , list the elements of $A \cup B$ .

List the elements of the set. -If $A = \{ x \mid x$ is an odd integer $\}$ and $B = \{ x \mid x$ is an even integer $\}$ , list the elements of $A \cup B$ .