Question 1

Solve the compound inequality. Express the solution using interval notation. Graph the solution set.
-$x < 2$ or $x < 8$

Accepted Answer

A)  $( - \infty , 2 ) \cup ( 8 , \infty )$
  
B)  $( - \infty , 8 )$
  
C)  $( 2,8 )$
  
D)  $( 2 , \infty )$
  
A)  $( - \infty , 2 ) \cup ( 8 , \infty )$
  
B)  $( - \infty , 8 )$
  
C)  $( 2,8 )$
  
D)  $( 2 , \infty )$

Question 2

Write interval notation.
-$\{ x \mid \leq x < 4 \}$

Accepted Answer

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

Question 3

Solve.
-Photography reprints cost $\$ 0.52$ each at a local photo shop. Through the mail, they cost $\$ 0.44$ each plus $\$ 1.20$ postage and handling. How many reprints must a customer purchase to make it less expensive to use mail order?

Accepted Answer

A)  $\{ n \mid n > 16$ reprints $\}$ 
B)  $\{ \mathrm { n } \mid \mathrm { n } > 15$ reprints $\}$ 
C)  $\{ n \mid n > 18$ reprints $\}$ 
D)  $\{ \mathrm { n } \mid \mathrm { n } > 19$ reprints $\}$ 
A)  $\{ n \mid n > 16$ reprints $\}$ 
B)  $\{ \mathrm { n } \mid \mathrm { n } > 15$ reprints $\}$ 
C)  $\{ n \mid n > 18$ reprints $\}$ 
D)  $\{ \mathrm { n } \mid \mathrm { n } > 19$ reprints $\}$

Question 4

Write interval notation.
-$$\{ x \mid x \leq - 4 \}$$

Accepted Answer

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

Question 5

Solve.
-$- 20 \leq - 3 z + 4 \leq - 2$

Accepted Answer

A)  $( 2,8 )$ 
B)  $[ 2,8 ]$ 
C)  $( - 8 , - 2 )$ 
D)  $[ - 8 , - 2 ]$ 
A)  $( 2,8 )$ 
B)  $[ 2,8 ]$ 
C)  $( - 8 , - 2 )$ 
D)  $[ - 8 , - 2 ]$

Question 6

Solve.
-$$- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 15 } < \frac { 1 } { 3 }$$

Accepted Answer

A)  $\left( - \frac { 4 } { 3 } , 2 \right)$ 
B)  $\left[ - \frac { 14 } { 9 } , \frac { 16 } { 9 } \right]$ 
C)  $\left[ - \frac { 4 } { 3 } , 2 \right)$ 
D)  $\left[ - \frac { 4 } { 3 } , 2 \right]$ 
A)  $\left( - \frac { 4 } { 3 } , 2 \right)$ 
B)  $\left[ - \frac { 14 } { 9 } , \frac { 16 } { 9 } \right]$ 
C)  $\left[ - \frac { 4 } { 3 } , 2 \right)$ 
D)  $\left[ - \frac { 4 } { 3 } , 2 \right]$

Question 7

Solve and graph.
-$5 x - 1  - 1$

Accepted Answer

A)  $[ 0,1 ]$
  
B)  $\varnothing$ 
C)  $( 0,1 )$
  
D)  $\{ 1 \}$
  
A)  $[ 0,1 ]$
  
B)  $\varnothing$ 
C)  $( 0,1 )$
  
D)  $\{ 1 \}$

Question 8

Write interval notation for the graph.
-

Accepted Answer

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

Question 9

Solve.
-In order for a chemical reaction to remain stable, its Celsius temperature $\mathrm { C }$ must be no more than $51.57 ^ { \circ } \mathrm { C }$. At what Fahrenheit temperatures F will the reaction remain stable. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Accepted Answer

A)  $\left\{ \mathrm { F } \mid \mathrm { F } \leq 10.87 ^ { \circ } \right\}$ 
B)  $\left\{ \mathrm { F } \mid \mathrm { F } \geq 10.87 ^ { \circ } \right\}$ 
C)  $\left\{ \mathrm { F } \mid \mathrm { F } \leq 124.83 ^ { \circ } \right\}$ 
D)  $\left\{ F \mid F \geq 124.83 ^ { \circ } \right\}$ 
A)  $\left\{ \mathrm { F } \mid \mathrm { F } \leq 10.87 ^ { \circ } \right\}$ 
B)  $\left\{ \mathrm { F } \mid \mathrm { F } \geq 10.87 ^ { \circ } \right\}$ 
C)  $\left\{ \mathrm { F } \mid \mathrm { F } \leq 124.83 ^ { \circ } \right\}$ 
D)  $\left\{ F \mid F \geq 124.83 ^ { \circ } \right\}$

Question 10

Graph and write interval notation.
-$2 < x < 6$

Accepted Answer

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

Question 11

Solve and graph.
-$4 x - 10 \leq 18$ and $2 x - 1 \geq 13$

Accepted Answer

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

Question 12

Solve and graph. Write the result in interval notation.
-$\frac { 5 } { 7 } x \geq 5$

Accepted Answer

A)  $[ 7 , \infty )$
  
B)  $[ 5 , \infty )$
  
C)  $( \infty , 7 ]$
  
D)  $( \infty , 5 ]$
  
A)  $[ 7 , \infty )$
  
B)  $[ 5 , \infty )$
  
C)  $( \infty , 7 ]$
  
D)  $( \infty , 5 ]$

Question 13

Solve.
-$$3 \geq - x > - 8$$

Accepted Answer

A)  $[ - 3,8 )$ 
B)  $[ 3,8 )$ 
C)  $( - 3,8 ]$ 
D)  $( - 8,3 ]$ 
A)  $[ - 3,8 )$ 
B)  $[ 3,8 )$ 
C)  $( - 3,8 ]$ 
D)  $( - 8,3 ]$

Question 14

Solve and graph. Write the result in interval notation.
-$\frac { 5 } { 7 } x < - 9$

Accepted Answer

A)  $\left( \infty , - \frac { 63 } { 5 } \right)$
  
B)  $\left( - \frac { 45 } { 7 } , \infty \right)$
  
C)  $\left( - \infty , \frac { 7 } { 45 } \right)$
  
D)  $\left( \infty , - \frac { 5 } { 63 } \right)$
  
A)  $\left( \infty , - \frac { 63 } { 5 } \right)$
  
B)  $\left( - \frac { 45 } { 7 } , \infty \right)$
  
C)  $\left( - \infty , \frac { 7 } { 45 } \right)$
  
D)  $\left( \infty , - \frac { 5 } { 63 } \right)$

Question 15

Solve and graph. Write the result in interval notation.
-$5 x \leq 40$

Accepted Answer

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

Question 16

Solve and graph.
-$9 x - 6 < 3 x \text { or } - 2 x \leq - 6$

Accepted Answer

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

Question 17

Solve.
-$1.2 x - 3 \geq 0.7 x + 15.5$

Accepted Answer

A)  $[ 37 , \infty )$ 
B)  $( - \infty , 37 )$ 
C)  $( 3.7 , \infty )$ 
D)  $( - \infty , 37 ]$ 
A)  $[ 37 , \infty )$ 
B)  $( - \infty , 37 )$ 
C)  $( 3.7 , \infty )$ 
D)  $( - \infty , 37 ]$

Question 18

Choose the number that is a solution of the inequality.
-$8 n + 4 > 7 n + 7$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  4 
A)  1 
B)  2 
C)  0 
D)  4

Question 19

Solve and graph. Write the result in interval notation.
-$0.25 a > 2$

Accepted Answer

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

Question 20

Write interval notation.
-$\{ x \mid \leq x \leq 6 \}$

Accepted Answer

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

Solve the compound inequality. Express the solution using interval notation. Graph the solution set. - $x < 2$ or $x < 8$

Write interval notation. - $\{ x \mid \leq x < 4 \}$

Solve. -Photography reprints cost $\$ 0.52$ each at a local photo shop. Through the mail, they cost $\$ 0.44$ each plus $\$ 1.20$ postage and handling. How many reprints must a customer purchase to make it less expensive to use mail order?

Write interval notation. - $\{ x \mid x \leq - 4 \}$

Solve. - $- 20 \leq - 3 z + 4 \leq - 2$

Solve. - $- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 15 } < \frac { 1 } { 3 }$

Solve and graph. - $5 x - 1 < 4$ and $x - 2 > - 1$

Write interval notation for the graph. -

Solve. -In order for a chemical reaction to remain stable, its Celsius temperature $\mathrm { C }$ must be no more than $51.57 ^ { \circ } \mathrm { C }$ . At what Fahrenheit temperatures F will the reaction remain stable. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

Graph and write interval notation. - $2 < x < 6$

Solve and graph. - $4 x - 10 \leq 18$ and $2 x - 1 \geq 13$ $Solve and graph. - 4 x - 10 \leq 18 and 2 x - 1 \geq 13$

Solve and graph. Write the result in interval notation. - $\frac { 5 } { 7 } x \geq 5$ $Solve and graph. Write the result in interval notation. - \frac { 5 } { 7 } x \geq 5$

Solve. - $3 \geq - x > - 8$

Solve and graph. Write the result in interval notation. - $\frac { 5 } { 7 } x < - 9$ $Solve and graph. Write the result in interval notation. - \frac { 5 } { 7 } x < - 9$

Solve and graph. Write the result in interval notation. - $5 x \leq 40$ $Solve and graph. Write the result in interval notation. - 5 x \leq 40$

Solve and graph. - $9 x - 6 < 3 x \text { or } - 2 x \leq - 6$ $Solve and graph. - 9 x - 6 < 3 x \text { or } - 2 x \leq - 6$

Solve. - $1.2 x - 3 \geq 0.7 x + 15.5$

Choose the number that is a solution of the inequality. - $8 n + 4 > 7 n + 7$

Solve and graph. Write the result in interval notation. - $0.25 a > 2$

Write interval notation. - $\{ x \mid \leq x \leq 6 \}$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 9: More on Inequalities

Solve the compound inequality. Express the solution using interval notation. Graph the solution set. - x<2x < 2x<2 or x<8x < 8x<8

Write interval notation. - {x∣≤x<4}\{ x \mid \leq x < 4 \}{x∣≤x<4}

Solve. -Photography reprints cost $0.52\$ 0.52$0.52 each at a local photo shop. Through the mail, they cost $0.44\$ 0.44$0.44 each plus $1.20\$ 1.20$1.20 postage and handling. How many reprints must a customer purchase to make it less expensive to use mail order?

Write interval notation. - {x∣x≤−4}\{ x \mid x \leq - 4 \}{x∣x≤−4}

Solve. - −20≤−3z+4≤−2- 20 \leq - 3 z + 4 \leq - 2−20≤−3z+4≤−2

Solve. - −13≤3x−115<13- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 15 } < \frac { 1 } { 3 }−31​≤153x−1​<31​

Solve and graph. - 5x−1<45 x - 1 < 45x−1<4 and x−2>−1x - 2 > - 1x−2>−1