Deck 4: Inequalities

Question 1

Solve the inequality and graph the solution set. $\frac { 7 - d } { - 2 } \leq - 7$

A) $( - 8 , \infty )$

B) $( - \infty , - 9 ]$

C) $( - \infty , - 7 ]$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Answer 1

$( - \infty , - 7 ]$

Question 2

Solve the inequality and graph the solution set. $- 2 s - 105 \leq - 7 s - 220$

A) $( - \infty , - 23 ]$

B) $( - \infty , - 23 )$

C) $( - \infty , - 24 ]$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Answer 2

$( - \infty , - 23 ]$

Question 3

Solve the inequality and graph the solution set. $11 x + 6 + 3 x \geq 12 + 13 x - 6$

A) $[ 4 , \infty )$

B) $[ 0 , \infty )$

C) $( - \infty , 5 )$

D) $[ - 4 , \infty )$

E) $\varnothing$

Answer 3

$[ 0 , \infty )$

Question 4

A school PTA wants to rent a dunking tank for its annual school fundraising carnival. The cost is $80.00 for the first three hours and then $18.50 for each additional hour or part thereof. How long can the tank be rented if up to $180 is budgeted for this expense?

A) 5 hr
B) 7 hr
C) 4 hr
D) 6 hr
E) 8 hr

Question 5

Solve the inequality and graph the solution set. $5 x < - 35$

A) $( - \infty , - 7 )$
B) $( - \infty , - 7 ]$

C) $( - 7 , \infty )$

D) $( - \infty , \infty )$
E) $\varnothing$

Question 6

Solve the inequality and graph the solution set.
$\frac { x - 7 } { 2 } - \frac { x - 1 } { 5 } \geq - \frac { x } { 4 }$

A) $[ 6 , \infty )$

B) $( - \infty , 6 ]$

C) $( 6 , \infty )$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 7

An excavating company charges $330 an hour for the use of a backhoe and $550 an hour for the use of a bulldozer. The company employs one operator for 40 hours per week to operate the machinery. If the company wants to bring in at least $18,500 each week from equipment rental, what is the maximum whole number of hours per week can it schedule the operator to use a backhoe?

A) 17 hr
B) 13 hr
C) 14 hr
D) 16 hr
E) 15 hr

Question 8

Solve the inequality and graph the solution set. $3 < \frac { 5 } { 3 } a - 2$

A) $( 4 , \infty )$

B) $[ 2 , \infty )$

C) $( 3 , \infty )$

D) $( \infty , \infty )$

E) $\varnothing$

Question 9

A student works two part-time jobs. He earns $7 an hour for working at the college library and $13 an hour for construction work. To save time for study, he limits his work to 25 hours a week. If he enjoys the work at the library more, how many hours can he work at the library and still earn at least $235 a week?

A) 12 hr
B) 13 hr
C) 14 hr
D) 15 hr
E) 16 hr

Question 10

Solve the inequality and write the solution set using interval notation. $5 b - 20 \geq - 25$

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

B) $( - 1 , \infty )$

C) $[ - 1 , \infty )$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 11

Solve the inequality and graph the solution set. $- 8 x + 7 > - 6 x - 1$

A) $( - \infty , 4 )$

B) $[ 4 , \infty )$

C) $( - \infty , 5 )$

D)
$( - \infty , \infty )$


E)
$\varnothing$

Question 12

A student has scores of 71, 73, and 90 on three government exams. What score does she need on a fourth exam to give her an average of 80 or better?

A) 83 or higher
B) 87 or higher
C) 84 or higher
D) 86 or higher
E) 85 or higher

Question 13

Solve the inequality and graph the solution set. $5 ( 3 + z ) > - 4 ( z + 3 )$

A) $( - 3 , \infty )$

B) $( - \infty , 3 )$

C) $( 3 , \infty )$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 14

Solve the inequality and graph the solution set. $- 7 t + 4 \leq 6$

A) $\left[ - \frac { 2 } { 7 } , \infty \right)$

B) $\left( - \frac { 2 } { 7 } , \infty \right)$

C) $\left( \frac { 2 } { 7 } , \infty \right)$

D) $\left( - \infty , \frac { 2 } { 7 } \right)$

E) $\varnothing$

Question 15

Solve the inequality and graph the solution set.
$- 10 ( h - 3 ) + 2 h \leq 9 ( 4 - h )$

A) $( - \infty , 6 ]$

B) $( - \infty , 10 ]$

C) $[ 6 , \infty )$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 16

Solve the inequality and graph the solution set.
$\frac { 1 } { 2 } y + 2 \geq \frac { 1 } { 3 } y - 4$

A) $( - \infty , - 37 ]$

B) $[ - 36 , \infty )$

C) $[ 36 , \infty )$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 17

Solve the inequality and graph the solution. $\frac { 9 - 3 b } { - 8 } < 3$

A) $( - \infty , 11 )$

B) $[ 11 , \infty )$

C) $( - \infty , - 12 ]$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 18

Solve the inequality and graph the solution set. $0.4 x + 0.33 \leq 0.1 x + 0.81$

A) $( - \infty , 1.7 ]$

B) $( - \infty , 1.6 ]$

C) $( - \infty , 1.8 )$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 19

Solve the inequality and graph the solution set. $10 x + 4 + 11 x > 2 - 11 x + 2$

A) $( 0 , \infty )$

B) $( - \infty , 0 ]$

C) $[ - 11 , \infty )$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 20

Solve the inequality and graph the solution set.
$\frac { 1 } { 2 } x + 9 \geq 7 + 4 x$

A) $\left[ \frac { 4 } { 7 } , \infty \right)$

B) $\left( - \infty , \frac { 4 } { 7 } \right]$

C) $\left( - \infty , \frac { 4 } { 7 } \right)$

D)
$( - \infty , \infty )$

E)
$\varnothing$

Question 21

The graph of a set of real numbers that is a portion of a number line is called a(n) _________.

Question 22

Solve the inequality: $\frac { 5 x - 2 } { - 3 } \geq 5$

A) $\left( - \infty , - \frac { 13 } { 5 } \right]$
B) $\left[ - \frac { 13 } { 5 } , \infty \right)$
C) $\left[ \frac { 17 } { 5 } , \infty \right)$
D) $\left( \infty , - \frac { 13 } { 5 } \right]$

Question 23

Write $- 3 \geq x$ in interval notation.

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

Question 24

is a symbol that representing positive ________.

Question 25

Solve and write solution set in interval notation: $8 x - 2 < x - 4$

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

Question 26

A student works two part-time jobs. He earns $8 an hour for working at the college library and $12 an hour for construction work. To save time for study, he limits his work to 25 hours a week. If he enjoys the work at the library more, how many hours can he work at the library and still earn at least $256 a week?
__________ hr

Question 27

are _________ symbols.

Question 28

Solve and write solution set in interval notation: $\frac { x } { 3 } - \frac { 1 } { 4 } < 2 x$

A) $\left( - \infty , - \frac { 3 } { 20 } \right)$
B) $\left( - \frac { 3 } { 20 } , \infty \right)$
C) $( - 3 , \infty )$
D) $( - \infty , - 3 )$

Question 29

Company A offers a monthly salary of $2400 plus a commission of 6% of the sales. Company B offers a monthly salary of $2900 plus a commission of 4% of the sales. How much must a person sell for Company A to be more money?

A) more than $2,500
B) more than $250
C) more than $25,000
D) none of these

Question 30

Minnie has invested $5000 at 2% annual interest. How much more must she invest at 3% so that her annual income is at least $1,000?

A) at least $2,000
B) at least $20,000
C) at least $30,000
D) at least $3,000

Question 31

Solve and graph the inequality: $- 2 x - 6 \leq 8$

A)
B)
C)
D)

Question 32

Write $- 2 \leq x$ in interval notation.

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

Question 33

$- 9 < - 5 x - 1 < - 3$ is an example of a __________ inequality in one variable.

A) linear
B) compound
C) double
D) quadratic

Question 34

Solve the inequality: $3 ( 3 x - 5 ) - 5 ( x - 4 ) \geq 4 x + 5$

A) no solution
B) $( - \infty , \infty )$
C) $( - \infty , 0 ]$
D) $[ 0 , \infty )$

Question 35

If $a < b$ and $c < 0$ , then ac ________ bc

A) <
B) >

Question 36

A school PTA wants to rent a dunking tank for its annual school fund-raising carnival. The cost is $90.00 for the first three hours and then $20.50 for each additional hour or part thereof. How long can the tank be rented if up to $185 is budgeted for this expense?
__________ hr

Question 37

Consider the costs of moving when Truck A costs a flat fee of $800 for 4 days and does not charge for mileage versus Truck B which costs $40 per day and 16 cents per mile. If the move takes 4 days, how many miles would Truck B have to be driven to make it more expensive than Truck A?

Question 38

An excavating company charges $330 an hour for the use of a backhoe and $550 an hour for the use of a bulldozer. The company employs one operator for 40 hours per week to operate the machinery. If the company wants to bring in at least $18,500 each week from equipment rental, how many hours per week can it schedule the operator to use a backhoe?
__________ hr

Question 39

Solve the inequality: $2 ( 7 x - 3 ) - 9 \geq 8 x - 6 + 6 x$

A) $( - \infty , \infty )$
B) no solution
C) $[ - 15 , \infty )$
D) $( - \infty , - 6 ]$

Question 40

A student has scores of 70, 71, and 89 on three government exams. What score does she need on a fourth exam to give her an average of 80 or better?
__________ or higher

Question 41

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 4 ( x + 2 ) \geq 16$ or $2 x + 5 < 9$

A) $( - \infty , 2 ]$

B) $( - \infty , - 6 ] \cup ( 2 , \infty )$

C) $[ - 6,2 )$

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

E) $( - 6,2 ]$

Question 42

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $2.4 x < - 21.6$ and $- 2 x < 20$

A) $( - \infty , - 10 )$

B) $[ - 10 , - 9 ]$

C) $( - 10 , - 9 )$

D) $( - 9 , \infty )$

E) $( - \infty , - 9 )$

Question 43

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 1 < - b + 4 < 5$

A) $( 5 , \infty )$

B) $[ - 1,5 )$

C) (-1,5)

D) $( - \infty , - 1 )$

E)
$\varnothing$

Question 44

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $4 ( x + 1 ) \leq 3 ( x + 2 )$ and $x + 12 < - 3$

A) $( - \infty , 2 ]$

B) $[ - 15,2 ]$

C) $( - 15,2 ]$

D) $( - 15,2 )$

E) $( - \infty , - 15 )$

Question 45

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $x \leq - 7$ or $x > 3$

A) $( - \infty , - 7 ] \cup ( 3 , \infty )$

B) $( 3 , \infty )$

C) $[ - 7,3 )$

D) $( - \infty , - 7 ]$

E) $\varnothing$

Question 46

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12$

A) $[ 7 , \infty )$

B) $\left[ \frac { 1 } { 7 } , \infty \right)$

C) $\left( - \infty , \frac { 1 } { 7 } \right]$

D) $\left[ \frac { 1 } { 7 } , 7 \right]$

E) $\varnothing$

Question 47

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $x - 3 < - 5$ or $x - 4 > 0$

A) $( - \infty , - 2 )$

B) $( - \infty , - 2 ) \cup ( 4 , \infty )$

C) $( 4 , \infty )$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 48

The __________ of two sets is the set of elements that are common to both sets, and the __________ of two sets is the set of elements that are in one set, or the other, or both.

A) union, intersection
B) inverse, intersection
C) intersection, union
D) complement, combination
E) combination, complement

Question 49

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $3 x + 1 < 7$ or $3 x - 1 > 23$

A) $( - \infty , 2 ) \cup ( 8 , \infty )$

B) $( 2,8 )$

C)
$( - \infty , 2 )$

D) $( 8 , \infty )$

E) $\varnothing$

Question 50

Solve the double inequality. Graph the solution set (if one exists) and write it using interval notation. $3 \leq x + 2 \leq 6$

A) $[ 4 , \infty )$

B) $[ 1,4 ]$

C) $( - \infty , 1 ]$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 51

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $2 x + 3 \geq 9$ and $- 2 ( x + 1 ) \geq - 8$

A) $[ - 3,3 ]$

B) $[ 3,3 ]$

C) $( - \infty , 3 )$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 52

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 3 x < - 4 x$ and $9 x > 8 x$

A) $( - \infty , 0 ) \cup ( 0 , \infty )$

B) $x = 0$

C) $( - \infty , 0 )$

D) $( 0 , \infty )$

E) $\varnothing$

Question 53

What is incorrect about the following work?
Explain and then give the correct solution.

Question 54

Two health insurance plans are offered to employees of a company. Plan I has a $600 deductible and then pays 70% of the rest of the cost versus Plan II that has a $2400 deductible and then pays 90% of the rest of the cost. What would annual medical costs have to be for Plan II to be the least expensive?

Question 55

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $8 ( x - 3 ) \geq 0$ and $- 4 x < 8$

A) $[ 3 , \infty )$

B) $( - 2,3 ]$

C) $( - \infty , 3 ]$

D) $( - 2 , \infty )$

E) $\varnothing$

Question 56

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $\frac { 1 } { 2 } x \leq 2$ and $0.75 x \geq - 6$

A) $( - 8,4 ]$

B) $[ - 8,4 )$

C) $[ - 8,4 ]$

D) (-8,4)

E) $\varnothing$

Question 57

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $25 > 3 x - 2 > 4$

A) $( - \infty , 2 ) \cup ( 9 , \infty )$

B) $( 9 , \infty )$

C) $( - \infty , 2 )$

D) $( - \infty , \infty )$

E) $( 2,9 )$

Question 58

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $x > - 3$ and $x \leq 5$

A) $[ - 5,3 )$

B) $[ - 3,5 )$

C) $( - 3,5 ]$

D) $( - \infty , \infty )$

E) $\varnothing$

Question 59

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 2 < - 2 ( x - 5 ) \leq 18$

A) $( - 6,4 ]$

B) $( - \infty , - 4 ] \cup ( 6 , \infty )$

C) $[ - 6,4 )$

D) $[ - 4,6 )$

E) $( - 4,6 ]$

Question 60

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $5 x - 5 > 5$ and $x + 2 \leq 10$

A) $( 2,8 ]$

B) $( - \infty , 2 ) \cup [ 8 , \infty )$

C) $( 2 , \infty )$

D) $( - \infty , 8 ]$

E) $( 2,8 )$

Question 61

Solve the compound inequality and write the answer in interval notation.

Question 62

Let and . Find .

Question 63

Solve: $7 x - 1 \geq 6$ or $\frac { x } { 6 } + 5 < 4$

A) $( - 6,1 ]$
B) $[ - 1 , \infty )$
C) $( - \infty , - 6 ) \cup [ 1 , \infty )$
D) $( - \infty , - 6 )$

Question 64

Solve the compound inequality and write the answer in interval notation. or

Question 65

Let and . Find .

Question 66

When two equations are joined by the word or , such as $x + 1 = 4$ or $x + 1 = - 4$ , we call the statement a(n) __________ statement.

A) compound
B) equality
C) opposite
D) value
E) absolute value

Question 67

When solving a compound inequality containing the word and , the solution set is the _________ of the solution sets of the inequalities.

Question 68

Let $A = \{ 7,10,11 \}$ and $B = \{ 10,11,13 \}$ . Find $A \cap B$ .

A) $\varnothing$
B) $( - \infty , \infty )$
C) $\{ 7,10,11,13 \}$
D) $\{ 10,11 \}$

Question 69

Solve, if possible: $- 6 x < - 18$ and $4 x + 1 \leq 9$

A) $\varnothing$
B) $( - \infty , \infty )$
C) $( - \infty , 2 ]$
D) $[ 2,3 )$

Question 70

Graph the solution set for $x < - 2$ and $x < 1$

A)
B)
C)
D)

Question 71

Solve the inequality $5 \leq x$ and $x \geq 7$ .

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

Question 72

Solve the equation. $| x | = 21$

A) $x = - 21,21$
B) $x = - 20$
C) $x = 21$
D) $x = - 20,20$
E) no solution

Question 73

What is incorrect about the inequality ?

Question 74

Solve, graph, and write in interval notation: Interval notation: __________

Question 75

The __________ of two sets is the set of elements that are common to both sets and the __________ of two sets is the set of elements that are in one set, or the other, or both.

Question 76

When solving an inequality containing the word or , the solution set is the ________ of the solution sets of the inequalities.

Question 77

Solve and graph the solution set: $- 1 > 3 x + 5 \geq - 4$

A)
B)
C)
D)

Question 78

Let $A = \{ 2,4,5 \}$ and $B = \{ 6,7,9 \}$ . Find $A \cup \bar { B }$ .

A) $( - \infty , \infty )$
B) $\{ 4,9 \}$
C) $\{ 2,4,5,6,7,9 \}$
D) $\varnothing$

Question 79

Solve the inequality: $- 2 < \frac { 5 x - 3 } { - 3 } < 3$

A) $\left( - \frac { 3 } { 5 } , 0 \right)$
B) $\left( \frac { 9 } { 5 } , - \frac { 6 } { 5 } \right)$
C) $\left( - \frac { 3 } { 5 } , \frac { 12 } { 5 } \right)$
D) $\left( - \frac { 6 } { 5 } , \frac { 9 } { 5 } \right)$

Question 80

The __________ of a number is its distance from 0 on a number line.

A) opposite
B) positive value
C) absolute value
D) value
E) opposite value