Question 1

Solve the absolute value equation.
-$\left| \frac { 4 x + 12 } { 3 } \right| = 4$

Accepted Answer

A)  6,0 
B)  $- 6,0$ 
C)  $- 6,6$ 
D)  $\varnothing$ 
A)  6,0 
B)  $- 6,0$ 
C)  $- 6,6$ 
D)  $\varnothing$ B

Question 2

Graph the solution of the system of linear inequalities.
-$\left\{ \begin{array} { l } 
y \leq - 3 x + 3 \
y \geq x - 7
\end{array} \right.$

Accepted Answer

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

Question 3

Match the inequality with its graph.
-$x > 2$

Accepted Answer

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

Question 4

Determine whether the ordered pair given is a solution of the linear inequality in two variables.
-$y \geq - x ; ( 16 , - 16 )$

Accepted Answer

A) True 
 B)False

Question 5

Solve the inequality. Graph the solution set.
-$| x - 3 | \geq 0$

Accepted Answer

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

Question 6

Solve the compound inequality. Graph the solution set.
-$5 x + 2 < 6 x + 4 < 7 x - 3$

Accepted Answer

A) $ - 2,7 )$
  
B)  $( - 2 , \infty )$
  
C) $( - 2,7 )$
  
D) $( 7 , \infty )$
  
A) $ - 2,7 )$
  
B)  $( - 2 , \infty )$
  
C) $( - 2,7 )$
  
D) $( 7 , \infty )$

Question 7

Solve the absolute value equation.
-$| 8 x + 3 | = 2$

Accepted Answer

A)  $- \frac { 1 } { 3 } , - \frac { 5 } { 3 }$ 
B)  $\frac { 1 } { 8 } , \frac { 5 } { 8 }$ 
C)  $\varnothing$ 
D)  $- \frac { 1 } { 8 } , - \frac { 5 } { 8 }$ 
A)  $- \frac { 1 } { 3 } , - \frac { 5 } { 3 }$ 
B)  $\frac { 1 } { 8 } , \frac { 5 } { 8 }$ 
C)  $\varnothing$ 
D)  $- \frac { 1 } { 8 } , - \frac { 5 } { 8 }$

Question 8

Graph the solution of the system of linear inequalities.
-$\left\{ \begin{array} { l } 
y  - \frac { 1 } { 2 } x - 1
\end{array} \right.$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  no solution
  
A) 
  
B) 
  
C) 
  
D)  no solution

Question 9

Solve the equation or inequality.
-$| 7 k - 5 | > - 7$

Accepted Answer

A)  $\left( - \infty , - \frac { 2 } { 7 } \right) \cup \left( \frac { 12 } { 7 } , \infty \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\left( - \frac { 2 } { 7 } , \frac { 12 } { 7 } \right)$ 
D)  $\left( \frac { 12 } { 7 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 2 } { 7 } \right) \cup \left( \frac { 12 } { 7 } , \infty \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\left( - \frac { 2 } { 7 } , \frac { 12 } { 7 } \right)$ 
D)  $\left( \frac { 12 } { 7 } , \infty \right)$

Question 10

Graph the inequality.
-$7 x-4 y \geq 0$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 11

Solve the inequality. Graph the solution set.
-$| 8 k - 6 | + 1 < 10$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 8 } \right) \cup \left( \frac { 15 } { 8 } , \infty \right)$
  
B)  $\left( - \infty , - \frac { 3 } { 8 } \right)$
  
C)  $\left( - \frac { 3 } { 8 } , \frac { 15 } { 8 } \right)$
  
D)  $\left( - \infty , \frac { 15 } { 8 } \right)$
  
A)  $\left( - \infty , - \frac { 3 } { 8 } \right) \cup \left( \frac { 15 } { 8 } , \infty \right)$
  
B)  $\left( - \infty , - \frac { 3 } { 8 } \right)$
  
C)  $\left( - \frac { 3 } { 8 } , \frac { 15 } { 8 } \right)$
  
D)  $\left( - \infty , \frac { 15 } { 8 } \right)$

Question 12

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 $A \cap B$.

Accepted Answer

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

Question 13

Determine whether the ordered pair given is a solution of the linear inequality in two variables.
-$x - y \leq 7 ; ( - 4 , - 13 )$

Accepted Answer

A) True 
 B)False

Question 14

Determine whether the ordered pair given is a solution of the linear inequality in two variables.
-$x \leq y - 8 ; ( - 1,4 )$

Accepted Answer

A) True 
 B)False

Question 15

Solve the absolute value equation.
-$| 3 x - 2 | = | x - 7 |$

Accepted Answer

A)  $- \frac { 5 } { 2 } , \frac { 3 } { 4 }$ 
B)  $\frac { 5 } { 2 } , - \frac { 9 } { 4 }$ 
C)  $\varnothing$ 
D)  $- \frac { 5 } { 2 } , \frac { 9 } { 4 }$ 
A)  $- \frac { 5 } { 2 } , \frac { 3 } { 4 }$ 
B)  $\frac { 5 } { 2 } , - \frac { 9 } { 4 }$ 
C)  $\varnothing$ 
D)  $- \frac { 5 } { 2 } , \frac { 9 } { 4 }$

Question 16

Solve.
-The formula for converting Fahrenheit temperatures to Celsius temperatures is $C = \frac { 5 } { 9 } ( F - 32 )$. Use this formula to solve the problem. In a certain city, the average temperature ranges from $- 29 ^ { \circ }$ to $10 ^ { \circ }$ Celsius. Use a compound inequality to convert these temperatures to Fahrenheit temperatures. If necessary, round to the nearest tenth of a degree.

Accepted Answer

A)  $- 20.2 ^ { \circ } \leq \mathrm { F } \leq 50 ^ { \circ }$ 
B)  $15.9 ^ { \circ } \leq \mathrm { F } \leq 37.6 ^ { \circ }$ 
C)  $- 52.2 ^ { \circ } \leq \mathrm { F } \leq 18 ^ { \circ }$ 
D)  $- 84.2 ^ { \circ } \leq \mathrm { F } \leq - 14 ^ { \circ }$ 
A)  $- 20.2 ^ { \circ } \leq \mathrm { F } \leq 50 ^ { \circ }$ 
B)  $15.9 ^ { \circ } \leq \mathrm { F } \leq 37.6 ^ { \circ }$ 
C)  $- 52.2 ^ { \circ } \leq \mathrm { F } \leq 18 ^ { \circ }$ 
D)  $- 84.2 ^ { \circ } \leq \mathrm { F } \leq - 14 ^ { \circ }$

Question 17

Solve the compound inequality. Graph the solution set.
-$0.3 < 0.2 x - 0.5 < 1.2$

Accepted Answer

A)  $( 4,8.5 )$
  
B)  $( - 1,3.5 )$
  
C)  $[ 4,8.5 ]$
  
D) $( 4,8.5 )$
  
A)  $( 4,8.5 )$
  
B)  $( - 1,3.5 )$
  
C)  $[ 4,8.5 ]$
  
D) $( 4,8.5 )$

Question 18

Solve the inequality. Graph the solution set.
-$|x+6| \leq 0$

Accepted Answer

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

Question 19

Graph the inequality.
-$x<5 y$

Accepted Answer

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

Question 20

Solve the equation or inequality.
-$- 9 x > - 36$ and $x + 9 > 11$

Accepted Answer

A)  $( - \infty , 2 ) \cup ( 4 , \infty )$ 
B)  $( 2,4 )$ 
C)  $\varnothing$ 
D)  $( 4 , \infty )$ 
A)  $( - \infty , 2 ) \cup ( 4 , \infty )$ 
B)  $( 2,4 )$ 
C)  $\varnothing$ 
D)  $( 4 , \infty )$

Solve the absolute value equation. - $\left| \frac { 4 x + 12 } { 3 } \right| = 4$

Graph the solution of the system of linear inequalities. - $\left\{ \begin{array} { l } y \leq - 3 x + 3 \\y \geq x - 7\end{array} \right.$ $Graph the solution of the system of linear inequalities. - \left\{ \begin{array} { l } y \leq - 3 x + 3 \\ y \geq x - 7 \end{array} \right.$

Match the inequality with its graph. - $x > 2$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $y \geq - x ; ( 16 , - 16 )$

Solve the inequality. Graph the solution set. - $| x - 3 | \geq 0$ $Solve the inequality. Graph the solution set. - | x - 3 | \geq 0$

Solve the compound inequality. Graph the solution set. - $5 x + 2 < 6 x + 4 < 7 x - 3$

Solve the absolute value equation. - $| 8 x + 3 | = 2$

Solve the equation or inequality. - $| 7 k - 5 | > - 7$

Graph the inequality. - $7 x-4 y \geq 0$ $Graph the inequality. - 7 x-4 y \geq 0$

Solve the inequality. Graph the solution set. - $| 8 k - 6 | + 1 < 10$

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 $A \cap B$ .

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $x - y \leq 7 ; ( - 4 , - 13 )$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $x \leq y - 8 ; ( - 1,4 )$

Solve the absolute value equation. - $| 3 x - 2 | = | x - 7 |$

Solve the compound inequality. Graph the solution set. - $0.3 < 0.2 x - 0.5 < 1.2$

Solve the inequality. Graph the solution set. - $|x+6| \leq 0$ $Solve the inequality. Graph the solution set. - |x+6| \leq 0$

Graph the inequality. - $x<5 y$

Solve the equation or inequality. - $- 9 x > - 36$ and $x + 9 > 11$

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 absolute value equation. - ∣4x+123∣=4\left| \frac { 4 x + 12 } { 3 } \right| = 4​34x+12​​=4

Graph the solution of the system of linear inequalities. - {y≤−3x+3y≥x−7\left\{ \begin{array} { l } y \leq - 3 x + 3 \\y \geq x - 7\end{array} \right.{y≤−3x+3y≥x−7​

Match the inequality with its graph. - x>2x > 2x>2

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - y≥−x;(16,−16)y \geq - x ; ( 16 , - 16 )y≥−x;(16,−16)

Solve the inequality. Graph the solution set. - ∣x−3∣≥0| x - 3 | \geq 0∣x−3∣≥0

Solve the compound inequality. Graph the solution set. - 5x+2<6x+4<7x−35 x + 2 < 6 x + 4 < 7 x - 35x+2<6x+4<7x−3

Solve the absolute value equation. - ∣8x+3∣=2| 8 x + 3 | = 2∣8x+3∣=2

Graph the solution of the system of linear inequalities. - {y<−12x+8y>−12x−1\left\{ \begin{array} { l } y < - \frac { 1 } { 2 } x + 8 \\y > - \frac { 1 } { 2 } x - 1\end{array} \right.{y<−21​x+8y>−21​x−1​

Solve the equation or inequality. - ∣7k−5∣>−7| 7 k - 5 | > - 7∣7k−5∣>−7

Graph the inequality. - 7x−4y≥07 x-4 y \geq 07x−4y≥0

Solve the inequality. Graph the solution set. - ∣8k−6∣+1<10| 8 k - 6 | + 1 < 10∣8k−6∣+1<10

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 \cap BA∩B .

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - x−y≤7;(−4,−13)x - y \leq 7 ; ( - 4 , - 13 )x−y≤7;(−4,−13)

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - x≤y−8;(−1,4)x \leq y - 8 ; ( - 1,4 )x≤y−8;(−1,4)

Solve the absolute value equation. - ∣3x−2∣=∣x−7∣| 3 x - 2 | = | x - 7 |∣3x−2∣=∣x−7∣

Solve the compound inequality. Graph the solution set. - 0.3<0.2x−0.5<1.20.3 < 0.2 x - 0.5 < 1.20.3<0.2x−0.5<1.2

Solve the inequality. Graph the solution set. - ∣x+6∣≤0|x+6| \leq 0∣x+6∣≤0

Graph the inequality. - x<5yx<5 yx<5y

Solve the equation or inequality. - −9x>−36- 9 x > - 36−9x>−36 and x+9>11x + 9 > 11x+9>11

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 absolute value equation. - $\left| \frac { 4 x + 12 } { 3 } \right| = 4$

Graph the solution of the system of linear inequalities. - $\left\{ \begin{array} { l } y \leq - 3 x + 3 \\y \geq x - 7\end{array} \right.$ $Graph the solution of the system of linear inequalities. - \left\{ \begin{array} { l } y \leq - 3 x + 3 \\ y \geq x - 7 \end{array} \right.$

Match the inequality with its graph. - $x > 2$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $y \geq - x ; ( 16 , - 16 )$

Solve the inequality. Graph the solution set. - $| x - 3 | \geq 0$ $Solve the inequality. Graph the solution set. - | x - 3 | \geq 0$

Solve the compound inequality. Graph the solution set. - $5 x + 2 < 6 x + 4 < 7 x - 3$

Solve the absolute value equation. - $| 8 x + 3 | = 2$

Solve the equation or inequality. - $| 7 k - 5 | > - 7$

Graph the inequality. - $7 x-4 y \geq 0$ $Graph the inequality. - 7 x-4 y \geq 0$

Solve the inequality. Graph the solution set. - $| 8 k - 6 | + 1 < 10$

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 $A \cap B$ .

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $x - y \leq 7 ; ( - 4 , - 13 )$

Determine whether the ordered pair given is a solution of the linear inequality in two variables. - $x \leq y - 8 ; ( - 1,4 )$

Solve the absolute value equation. - $| 3 x - 2 | = | x - 7 |$

Solve the compound inequality. Graph the solution set. - $0.3 < 0.2 x - 0.5 < 1.2$

Solve the inequality. Graph the solution set. - $|x+6| \leq 0$ $Solve the inequality. Graph the solution set. - |x+6| \leq 0$

Graph the inequality. - $x<5 y$

Solve the equation or inequality. - $- 9 x > - 36$ and $x + 9 > 11$