Deck 2: Linear Equations

Question 1

Determine whether the given equation is linear.

Answer 1

A

Question 2

Solve by using the multiplication property of equality.
-58.1 = -8.3c

A) {7.0}
B) {2.0}
C) {-49.8}
D) {49.8}

Answer 2

A

Question 3

Determine whether the given equation is linear.
-2(x + 4) = 7

A) Linear
B) Nonlinear

Answer 3

A

Question 4

Determine whether the given value is a solution of the equation.
p = 7

A) Yes
B) No

Question 5

Determine whether the given equation is linear.

Question 6

Determine whether the given equation is linear.

Question 7

Determine whether the given equation is linear.
9x + 6 = 6

A) Linear
B) Nonlinear

Question 8

Determine whether the given value is a solution of the equation.
m = 4

A) Yes
B) No

Question 9

Solve by using the multiplication property of equality.
-x = 33

A) {33}
B) {-33}
C) {1}
D) {0}

Question 10

Determine whether the given equation is linear.

Question 11

Solve by using the multiplication property of equality.
-3x = -12

A) {2}
B) {-9}
C) {4}
D) {9}

Question 12

Determine whether the given value is a solution of the equation.
p = 12

A) Yes
B) No

Question 13

Determine whether the given equation is linear.
8x = 24

A) Linear
B) Nonlinear

Question 14

Determine whether the given value is a solution of the equation.
y = 4

A) Yes
B) No

Question 15

Solve by using the multiplication property of equality.
-6a = 24

A) {30}
B) {1}
C) {-30}
D) {-4}

Question 16

Determine whether the given value is a solution of the equation.

Question 17

Determine whether the given equation is linear.

Question 18

Determine whether the given equation is linear.
-2 = 4x + 7

A) Linear
B) Nonlinear

Question 19

Solve by using the multiplication property of equality.
- 16 x = -3

A) {-10}
B) {-9}
C) {0}
D) {18}

Question 20

Determine whether the given value is a solution of the equation.
p = 7

A) Yes
B) No

Question 21

Choose the one alternative that best completes the statement or answers the question.
Solve.

Question 22

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write a linear equation that can be solved using the addition property of equality and that
has x = -7 as a solution.

Question 23

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write an equation that requires the use of the multiplication property of equality, where
both sides must be multiplied by 100 and where the solution isnʹt an integer.

Question 24

Choose the one alternative that best completes the statement or answers the question.
Solve.
4n - 9 = 27

A) {9}
B) {36}
C) {32}
D) {15}

Question 25

Choose the one alternative that best completes the statement or answers the question.
Solve.

Question 26

Solve the problem.

Question 27

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write a linear equation that can be solved using the multiplication property of equality
and that has

Question 28

Solve the problem.

Question 29

Choose the one alternative that best completes the statement or answers the question.
Solve.
8r + 7 = 79

A) {64}
B) {2}
C) {68}
D) {9}

Question 30

Solve the problem.

Question 31

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
What is the Multiplication Property of Equality?

Question 32

Choose the one alternative that best completes the statement or answers the question.
Solve.

Question 33

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write an equation that requires the use of the multiplication property of equality, where
both sides must be multiplied by

Question 34

Solve the problem.

Question 35

Solve by using the multiplication property of equality.
The Smith family is planning a 245-mile trip. They plan to travel at an average speed of 35 miles per hour. Determine the number of hours the trip will take.

A) 35 = 245x; 9 hours
B) 35 = 245x; 8 hours
C) 245 = 35x; 7 hours
D) 245 = 35x; 6 hours

Question 36

Choose the one alternative that best completes the statement or answers the question.
Solve.

Question 37

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
While solving an equation, why canʹt you multiply both sides of the equation by zero?

Question 38

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Your friend solves an equation as follows:

Question 39

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
What is the first step to solve an equation in the form

Question 40

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
What is the first step to solve an equation in the form b + x = a? What is the solution of the
equation?

Question 41

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of two consecutive even integers is 66. Find the larger number.

A) 34
B) 42
C) 28
D) 30

Question 42

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write a linear equation that has m = 5 as a solution.

Question 43

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write the steps you would use to solve this equation: 4(x - 1) + 6x = -7x.

Question 44

Solve the problem.
A car rental agency advertised renting a luxury, full-size car for $24.95 per day and $0.19 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to
Spend.

A) 5 miles
B) 658 miles
C) 905 miles
D) 66 miles

Question 45

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of three consecutive odd integers is 195. Find the integers.

A) 58 59 60
B) 63 65 67
C) 65 67 69
D) 67 69 71

Question 46

Solve the problem.
A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joeʹs phone bill was $63 under this promotional deal, how many minutes of phone
Calls did he make? Round to the nearest integer, if necessary.

A) 2 min
B) 960 min
C) 1560 min
D) 10 min

Question 47

Solve the problem.

Question 48

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of twice a number and 17 less than the number is the same as the difference between -33 and the number. What is the number?

A) -8B)-3C)-4D)-5

Question 49

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
If 5 is added to a number and the sum is doubled, the result is -16 less than the number. Find the number.

A) -21
B) 6
C) -26
D) 26

Question 50

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of the page numbers on the facing pages of a book is 341. Find the larger page number.

A) 181
B) 166
C) 171
D) 169

Question 51

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The difference between two positive integers is 54. One integer is three times as great as the other. Find the integers.

A) 81 and 135
B) 27 and 54
C) 27 and 81
D) 54 and 81

Question 52

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Write a linear equation with parentheses that is a contradiction.

Question 53

Solve the problem.
If -14 is added to a number and the sum is doubled, the result is 12 less than the number. Find the number.

A) -40
B) 16
C) 26
D) 40

Question 54

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of two consecutive integers is -389. Find the larger integer.

A) -194
B) -196
C) -193
D) -195

Question 55

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Find the missing value such that x = 3 is a solution of 8x - 3 = ?.

Question 56

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The sum of three consecutive integers is 384. Find the integers.

A) 126 128 130
B) 128 129 130
C) 126 127 128
D) 127 128 129

Question 57

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
The solution set for the equation 6(4s - 3) = 24s - 18 is given as 0. Is this correct? Explain.

Question 58

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Find the missing value such that x = 5 is a solution to 4x + 19x - 6 = ? + 5.

Question 59

Solve the problem.
The sum of twice a number and 10 less than the number is the same as the difference between -2 and the number. What is the number?

A) 4
B) 3
C) 1
D) 2

Question 60

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
Find the mistake in the following solution.

Question 61

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
If three times the smaller of two consecutive integers is added to four times the larger, the result is 109. Find the smaller integer.

A) 45
B) 14
C) 16
D) 15

Question 62

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the measure of an angle such that the difference between its supplement and 3 times its complement is 6°.

Question 63

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A triangular lake-front lot has a perimeter of 1100 feet. One side is 300 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.

A) 200 feet, 500 feet, 700 feet
B) 100 feet, 200 feet, 300 feet
C) 200 feet, 200 feet, 200 feet
D) 100 feet, 400 feet, 600 feet

Question 64

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A rectangular Persian carpet has a perimeter of 176 inches. The length of the carpet is 18 inches more than the width. What are the dimensions of the carpet?

A) 79 inches, 97 inches
B) 70 inches, 88 inches
C) 35 inches, 53 inches
D) 53 inches, 71 inches

Question 65

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the measure of an angle such that the sum of the measures of its complement and its supplement is 174°.

Question 66

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.

Question 67

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the measure of an angle whose supplement is 3 times the measure of its complement.

Question 68

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The complement of an angle measures 52° less than the angle. Find the measure of the angle.

Question 69

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the measure of an angle if its supplement measures 265° less than 6 times its complement.

Question 70

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A square plywood platform has a perimeter which is 6 times the length of a side, decreased by 8. Find the length of a side.

A) 4
B) 1
C) 6
D) 2

Question 71

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A circle has a circumference of 26π meters. Find the radius of the circle.

A) 4 meters
B) 26 meters
C) 7 meters
D) 13 meters

Question 72

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Two angles of a triangle are 50° and 100°. What is the measure of the third angle?

Question 73

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the length of a rectangular lot with a perimeter of 136 meters if the length is 6 meters more than the width.

A) 31 meters
B) 74 meters
C) 68 meters
D) 37 meters

Question 74

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
DGʹs Plumbing and Heating charges $50 plus $60 per hour for emergency service. Bill remembers being billed just over $200 for an emergency call. How long to the nearest hour was the plumber at
Billʹs house?

A) 11 hours
B) 13 hours
C) 4 hours
D) 3 hours

Question 75

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Find the measure of an angle, if its supplement measures 51° more than twice its complement.

Question 76

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
If the first and third of three consecutive odd integers are added, the result is 63 less than five times the second integer. Find the third integer.

A) 19
B) 42
C) 23
D) 21

Question 77

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A car rental company has two rental rates. Rate 1 is $72 per day plus $0.18 per mile. Rate 2 is $144 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to
Drive to pay less by taking Rate 2?

A) More than 5600 miles
B) More than 39,900 miles
C) More than 78,400 miles
D) More than 19,600 miles

Question 78

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
The perimeter of a rectangular room is 196 feet. Find the length and width of the room if the length is 8 feet longer than twice the width.

A) width = 30 feet; length = 68 feet
B) width = 35 feet; length = 78 feet
C) width = 45 feet; length = 53 feet
D) width = 60 feet; length = 136 feet

Question 79

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A rectangular horse pen is to be fenced and divided into five partitions as shown. The length of the fenced-in area is to be twice the width, and the total amount of fencing to be used is 250 feet. Find
The length and width of the fenced-in area.

A) length = 55.6 feet, width = 27.8 feet
B) length = 22.4 feet, width = 11.2 feet
C) length = 27 feet, width = 25 feet
D) length = 50 feet, width = 25 feet

Question 80

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A bag of marbles has twice as many blue marbles as green marbles, and the bag has at least 45 marbles in it. At least how many green marbles does it have?

A) At least 23 green marbles
B) At least 30 green marbles
C) At least 16 green marbles
D) At least 15 green marbles