Deck 9: More on Inequalities

Question 1

Write interval notation for the graph.

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

Answer 1

D

Question 2

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

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

Answer 2

D

Question 3

Choose the number that is a solution of the inequality.
a $- 5 < - 8$

A) $- 4$
B) 1
C) 4
D) $- 1$

Answer 3

A

Question 4

Choose the number that is a solution of the inequality.
$f - 12 < - 4$

A) 10
B) 7
C) 8
D) 11

Question 5

Write interval notation.
$\{ x \mid x \geq \}$

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

Question 6

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

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

Question 7

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

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

Question 8

Write interval notation for the graph.

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

Question 9

Write interval notation.
$\{ x \mid < x < \}$

A) $( 3,7 )$
B) $[ 3,7 )$
C) $( 3,7 ]$
D) $[ 3,7 ]$

Question 10

Write interval notation for the graph.

A) $( - \infty , 0 )$
B) $( 0 , \infty )$
C) $( - \infty , 0 ]$
D) $[ 0 , \infty )$

Question 11

Write interval notation for the graph.

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

Question 12

Write interval notation for the graph.

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

Question 13

Choose the number that is a solution of the inequality.
$- 3 n - 3 \leq - 4 n + 2$

A) 7
B) 6
C) 8
D) 5

Question 14

Write interval notation for the graph.

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

Question 15

Write interval notation for the graph.

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

Question 16

Write interval notation.
$\{ x \mid x < 2 \}$

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

Question 17

Write interval notation.
$\{ x \mid x > - 5 \}$

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

Question 18

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

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

Question 19

Choose the number that is a solution of the inequality.
$5 t + 9 \geq 4 t - 2$

A) $- 12$
B) $- 11$
C) $- 14$
D) $- 13$

Question 20

Write interval notation for the graph.

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

Question 21

Solve.
$1.1 x + 2.9 > 0.3 x + 1.22$

A) $( - 2.2 , \infty )$
В) $( - \infty , - 2.2 )$
C) $( - 2.1 , \infty )$
D) $( - \infty , - 2.1 )$

Question 22

Solve and graph. Write the result in interval notation.
$$9 x < - 54$$

A) $( - \infty , - 6 ]$

B) $( - \infty , - 6 )$

C) $( - 6 , \infty )$

D) $[ - 6 , \infty )$

Question 23

Solve.
$$2 ( 6 x + 8 ) \geq 2 ( 4 x + 24 )$$

A) $[ 16 , \infty )$
В) $( - \infty , 8 ]$
C) $[ 8 , \infty )$
D) $( - \infty , 16 ]$

Question 24

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

A) $( - \infty , 8 )$

B) $[ 8 , \infty )$

C) $( - \infty , 8 ]$

D) $( 8 , \infty )$

Question 25

Solve and graph. Write the result in interval notation.
$$f - 12 \leq - 4$$

A) $[ 8 , \infty )$

B) $( - \infty , 8 )$

C) $( 8 , \infty )$

D) $( - \infty , 8 ]$

Question 26

Solve and graph. Write the result in interval notation.
$$f - 4 < 8$$

A) $( - \infty , 12 )$

B) $( - \infty , 12 ]$

C) $( 12 , \infty )$

D) $[ 12 , \infty )$

Question 27

Solve and graph. Write the result in interval notation.
$$x - 10 < - 6$$

A) $( 4 , \infty )$

B) $[ 4 , \infty )$

C) $( - \infty , 4 ]$

D) $( - \infty , 4 )$

Question 28

Solve.
$7 x + 6 \geq 5 x + 2$

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

Question 29

Solve and graph. Write the result in interval notation.
$$a + 10 > 9$$

A) $( - \infty , - 1 ]$

В) $( - \infty , - 1 )$

C) $[ - 1 , \infty )$

D) $( - 1 , \infty )$

Question 30

Solve.
$$- 8 x - ( 4 x + 5 ) > 3 - ( 2 x + 9 )$$

A) $\left( \frac { 1 } { 10 } , \infty \right)$
B) $\left( \infty , - \frac { 7 } { 2 } \right)$
C) $\left( \pi , \frac { 1 } { 10 } \right)$
D) $\left( \infty , - \frac { 7 } { 10 } \right)$

Question 31

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

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

Question 32

Solve.
$$4 ( 3 x + 3 ) - 38 \leq 6 x - 2$$

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

Question 33

Solve.
$$- 5 ( \mathrm { k } - 5 ) < - 7 + ( - 6 \mathrm { k } + 9 )$$

A) $(\infty, 23 )$
В) $( \infty,9 )$
C) $(\infty, - 7 )$
D) $(\infty,-23)$

Question 34

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

A) $[ 7 , \infty )$

B) $[ 5 , \infty )$

C) $( \infty , 7 ]$

D) $( \infty , 5 ]$

Question 35

Solve.
$- 0.2 x \geq - 0.9$

A) $[ 4.5 , \infty )$
B) $( - \infty , 4.5 ]$
C) $( - \infty , - 0.7 ]$
D) $[ 0.7 , \infty )$

Question 36

Solve.
$$3 x + 9 < 24$$

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

Question 37

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

A) $[ 8 , \infty )$

B) $( - \infty , 8 )$

C) $( - \infty , 8 ]$

D) $( 8 , \infty )$

Question 38

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

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 39

Solve.
$$- \frac { 4 } { 5 } x \leq - \frac { 10 } { 11 }$$

A) $\left( - \infty , \frac { 8 } { 11 } \right]$
B) $\left( - \infty , \frac { 25 } { 22 } \right]$
C) $\left[ \frac { 25 } { 22 } , \infty \right]$
D) $\left[ \frac { 8 } { 11 } , \infty \right]$

Question 40

Solve.
$15 a - 15 > 5 ( 2 a - 9 )$

A) $( - \infty , 15 )$
В) $( - \infty , - 6 )$
C) $( - 6 , \infty )$
D) $( 15 , \infty )$

Question 41

Solve.
Jon has 1155 points in his math class. He must have $86 \%$ of the 1500 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the term to receive credit for the class?

A) 345 points
B) 135 points
C) 993 points
D) 1290 points

Question 42

Solve.
$$54 - ( 5 x + 4 ) \leq 2 ( x - 5 ) + 5 x$$

A) $\left( \infty , \frac { 17 } { 3 } \right]$
B) $( \infty , 5 ]$
C) $\left[ \frac { 17 } { 3 } , \infty \right]$
D) $[ 5 , \infty )$

Question 43

Solve.
$$\frac { 1 } { 6 } ( 12 x + 66 ) - 19 > - \frac { 1 } { 4 } ( 8 x - 32 )$$

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

Question 44

Solve.
$$\frac { 5 } { 3 } ( 5 x - 3 ) > 35$$

A) $\left( \infty , \frac { 24 } { 5 } \right)$
B) $\left( \infty , \frac { 18 } { 5 } \right)$
C) $\left( \frac { 18 } { 5 } , \infty \right)$
D) $\left( \frac { 24 } { 5 } , \infty \right)$

Question 45

Solve.
$$\frac { 1 } { 2 } ( x + 2 ) > \frac { 1 } { 6 } ( 5 x + 4 )$$

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

Question 46

Solve.
$$- 4 ( 2 x + 1 ) \geq 3 [ 3 x - 2 ( x + 1 ) ]$$

A) $\left[ - \infty , - \frac { 2 } { 11 } \right]$
B) $\left[ \frac { 2 } { 11 } , \infty \right)$
C) $\left[ - \infty , \frac { 2 } { 11 } \right]$
D) $( - \infty , - 2 ]$

Question 47

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?

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 48

Find the indicated intersection or union.
$\{ q , s , u , v , w , x , y , z \} \cup \{ q , s , y , z \}$

A) $\{ s , u , v , w , x , z \}$
B) $\{ \mathrm { s } , \mathrm { u } , \mathrm { w } \}$
C) $\{ \mathrm { v } , \mathrm { x } \}$
D) $\{ q , s , u , v , w , x , y , z \}$

Question 49

Find the indicated intersection or union.
$\{ \mathrm { q } , \mathrm { s } , \mathrm { u } , \mathrm { v } , \mathrm { w } , \mathrm { x } , \mathrm { y } , \mathrm { z } \} \cap \{ \mathrm { s } \}$

A) $\{ s , u , w \}$
B) $[ \mathrm { s } \}$
C) $\{ v , x \mid$
D) $\{ q , s , u , v , w , x , y \}$

Question 50

Solve.
A salesperson has two job offers. Company A offers a weekly salary of $\$ 360$ plus commission of $12 \%$ of sales. Company B offers a weekly salary of $\$ 720$ plus commission of $6 \%$ of sales. What is the amount of sales above which Company A's offer is the better of the two?

A) $\$ 6100$
B) $\$ 3000$
C) $\$ 12,000$
D) $\$ 6000$

Question 51

Solve.
Company A rents copiers for a monthly charge of $\$ 160$ plus 8 cents per copy. Company B rents copiers for a monthly charge of $\$ 320$ plus 4 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

A) 4100 copies
B) 2000 copies
C) 8000 copies
D) 4000 copies

Question 52

Solve.
The equation $y = 0.005 x + 0.30$ can be used to determine the profit $y$ , in dollars, of producing $x$ items. How many items $x$ must be produced so the profit will be at least $\$ 1273$ ?

A) $\{ x \mid 0 < x \leq 254,539 \}$
B) $\{ x \mid x \geq 254,540 \}$
C) $\{ x \mid x \geq 254,660 \}$
D) $\{ x \mid x \geq 253,540 \}$

Question 53

Solve.
$$\frac { 1 } { 10 } ( 3 x + 4 ) \leq - \frac { 1 } { 2 } + \frac { 1 } { 5 } ( 6 x + 1 )$$

A) $\left( \frac { 7 } { 9 } , \infty \right)$
B) $\left[ - \frac { 7 } { 9 } , \infty \right)$
C) $\left[ \frac { 7 } { 9 } , \infty \right)$
D) $\left[ - \infty , \frac { 7 } { 9 } \right]$

Question 54

Find the indicated intersection or union.
$\{ 4,9,14,16,23 \} \cap \{ 9,16,23,28 \}$

A) $\{ 4,9,16,23 \}$
B) $\{ 4,9,14,16,23,28 \}$
C) $\{ 9,16,23 \}$
D) $\{ 9,16,23,28 \}$

Question 55

Solve.
$$0.2 ( 4 x - 3 ) < 1.2 - ( x + 2 )$$

A) $\left( \infty , - \frac { 1 } { 9 } \right)$
B) $\left( \frac { 19 } { 9 } , \infty \right)$
C) $\left( \infty , \frac { 19 } { 9 } \right)$
D) $\left( - \frac { 1 } { 9 } , \infty \right)$

Question 56

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. $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

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 57

Solve.
$$3 ( 3 x + 1 ) < 5 - 5 ( 3 x - 3 )$$

A) $\left( \frac { 17 } { 24 } , \infty \right)$
B) $\left(\infty \frac{5}{24}\right)$
C) $\left[ - \frac { 5 } { 24 } , \infty \right)$
D) $\left(\infty, \frac{17}{24}\right)$ .

Question 58

Find the indicated intersection or union.
$\{ q , s , u , v , w , x , y , z \} \cap \{ q , s , y , z \}$

A) $\{ q , s , u , v , w , y \}$
B) $\{ s , u , v , w , x , z \}$
C) $\{ v , x \}$
D) $\{ q , s , y , z \}$

Question 59

Solve.
In order for a chemical reaction to take place, the Fahrenheit temperature F of the reagents must be at least $184.81 ^ { \circ } \mathrm { F }$ . At what Celsius temperatures $\mathrm { C }$ will the reaction occur? $\left( \mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \right)$

A) $\left\{ C \mid C \geq 364.66 ^ { \circ } \right\}$
B) $\left\{ \mathrm { C } \mid \mathrm { C } \leq 84.89 ^ { \circ } \right\}$
C) $\left\{ \mathrm { Cl } \mathrm { C } \geq 84.89 ^ { \circ } \right\}$
D) $\left\{ \mathrm { C } \mid \mathrm { C } < 364.66 ^ { \circ } \right\}$

Question 60

Find the indicated intersection or union.
$\{ 1,8,14,18 \} \cup \{ 8,18,24,30 \}$

A) $\{ 8,18,24 \}$
B) $\{ 1,8,14,18,24,30 \}$
C) $\{ 1,8,18,24 \}$
D) $\{ 8,18 \}$

Question 61

Graph and write interval notation.
$x \leq 2$ and $x \geq - 2$

A) $[ - 2,2 )$

B) $[ - 2,2 ]$

C) $( - 2,2 ]$

D) $( - 2,2 )$

Question 62

Graph and write interval notation.
$$x > 0 \text { and } x < 5$$

A) $[ 0,5 )$

B) $[ 0,5 ]$

C) $( 0,5 ]$

D) $( 0,5 )$

Question 63

Graph and write interval notation.
$$x < 3 \text { and } x > - 1$$

A) $( - 1,3 )$

B) $[ - 1,3 )$

C) $[ - 1,3 ]$

D) $( - 1,3 ]$

Question 64

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

A) $[ 0,1 ]$

B) $\varnothing$

C) $( 0,1 )$

D) $\{ 1 \}$

Question 65

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

A) $( 7 , \infty )$

B) $[ 7 , \infty )$

C) $\{ 7 \}$

D) $( - \infty , 7 )$

Question 66

Graph and write interval notation.
$$- 1 \leq x \leq 3$$

A) $( - 1,3 )$

B) $( - 1,3 ]$

C) $[ - 1,3 ]$

D) $[ - 1,3 )$

Question 67

Solve and graph.
$- 15 < 7 x - 1$ and $5 x - 9 < 1$

A) $( - 2,2 ]$

B) $[ - 2,2 ]$

C) $( - 2,2 )$

D) $[ - 2,2 )$

Question 68

Solve and graph.
$4 x > 4$ and $x + 5 < 5$

A) $( - 1 , \infty )$

B) $( 0,1 )$

C) $\varnothing$
D) $( - 1,0 )$

Question 69

Solve and graph.
$22 \leq 8 x - 2$ and $5 x - 7 < 28$

A) $( 3,7 ]$

B) $[ 3,7 )$

C) $( 3,7 )$

D) $[ 3,7 ]$

Question 70

Find the indicated intersection or union.
$\{ q , s , u , v , w , x \} \cap \varnothing$

A) $\{ q , s , u , v , w \}$
B) $\{ q \}$
C) $\varnothing$
D) $\{ \mathrm { q } , \mathrm { s } , \mathrm { u } , \mathrm { v } , \mathrm { w } , \mathrm { x } \}$

Question 71

Find the indicated intersection or union.
$\{ v , w , x , y , z \} \cup \{ q , s , y , z \}$

A) $\{ q , s , u , v , w , x , y \}$
B) $\{ \mathrm { s } , \mathrm { u } , \mathrm { w } \}$
C) $\{ q , s , v , w , x , y , z \}$
D) $\{ s , u , v , w , x , z \}$

Question 72

Solve.
$6 < 2 x \leq 12$

A) $[ - 3 , - 6 )$
B) $( 3,6 ]$
C) $[ 3,6 )$
D) $( - 3 , - 6 ]$

Question 73

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

A) $[ - 6 , - 2 )$

B) $( - 6 , - 2 )$

C) $( - 6 , - 2 ]$

D) $[ - 6 , - 2 ]$

Question 74

Solve and graph.
$6 x + 3 \geq - 3$ and $9 x - 4 \geq 14$

A) $[ - 1 , \infty )$

B) $( - \infty , - 1 ] \cup [ 2 , \infty )$

C) $[ - 1,2 ]$

D) $[ 2 , \infty )$

Question 75

Find the indicated intersection or union.
$\{ q , s , u , v , w , x \} \cup \varnothing$

A) $\{ q \}$
B) $\{ q , s , u , v , w , x \}$
C) $\varnothing$
D) $\{ \mathrm { q } , \mathrm { s } , \mathrm { u } , \mathrm { v } , \mathrm { w } \}$

Question 76

Solve and graph.
$2 x + 5 \geq 11$ and $2 x + 5 \leq 19$

A) $( 3,7 ]$

B) $[ 3,7 )$

C) $( 3,7 )$

D) $[ 3,7 ]$

Question 77

Solve and graph.
$$6 x + 2 < - 16 \text { and } 4 - 8 x > - 4$$

A) $( - \infty , 1 )$

B) $( - \infty , - 3 )$

C) $( - \infty , - 3 ) \cup ( 1 , \infty )$

D) $( - 3,1 )$

Question 78

Graph and write interval notation.
$x \geq 2$ and $x \geq - 3$

A) $[ 2 , \infty )$

B) $( - \infty , - 3 ]$

C) $( - \infty , 2 ]$

D) $( 2 , \infty )$

Question 79

Solve.
$$- 6 < x + 9 < 5$$

A) $( 3,14 )$
В) $( - 15,14 )$
C) $( - 15 , - 4 )$
D) $( - 14 , - 3 )$

Question 80

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

A) $( 2,6 ]$

B) $[ 2,6 )$

C) $( 2,6 )$

D) $[ 2,6 ]$