Free Printable Equations and Inequalities with Variables on Both Sides

1.

5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

2.

7x - 4 = 3 + 8x

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

3.

f - 4 = 6f + 26

a)

f = -5

b)

f = 5

c)

f = 6

d)

f = -6

4.

10x + 9 = 4x - 9

a)

0

b)

3

c)

-3

d)

-18

5.

-5k + 10 = -2k - 14

a)

8

b)

-8

c)

2

d)

-2

6.

6(5g+ 2)=30g

a)

g=2

b)

g=12

c)

all real numbers

d)

no solution

7.

5(2x -1) = -5+ 10x

a)

x = 5

b)

x = 0

c)

all real numbers

d)

no solution

8.

Solve for the variable.

22+2a=37+6+a

a)

a = 21

b)

a = 5

c)

a = -5

d)

a = -16

9.

Solve for the variable.

8-3a+12=2a

a)

a = 4

b)

a = 1

c)

a = 3

d)

a = 5

10.

Solve for the variable.

10x + 9 = 4x - 9

a)

x = 18

b)

x = 3

c)

x = -3

d)

x = -18

11.

What is the first step to solve this equation?

3x + 6 = 10 + 3x + 4x

a)

Add 4x to both sides of the equation

b)

Combine like terms 3x and 4x on the same side of the equation

c)

Add 3x and 6 to get 9x

d)

Add 6 and 10 to get 16

12.

What is the first step in solving the equation 2a - 4(a - 5) = 10

a)

Add the 2a and a

b)

Add 4 to both sides

c)

Distribute +4 to the a and -5

d)

Distribute -4 to a and -5

13.

3(x - 1) = 2x + 9

a)

Infinite Solutions

b)

No Solution

c)

x = 12

d)

x = -3

14.

Solve.

24k-72=3(8k-16)

a)

x = 3

b)

x = -3

c)

no solutions

d)

all real numbers

15.

2(x + 6) + 3 = 9 + 5x

a)

16

b)

2

c)

-8

d)

-10

16.

Solve for f:
f - 4 = 6f + 26

a)

f = -5

b)

f = 5

c)

f = 6

d)

f = -6

17.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

18.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

19.

Solve the equation:
7x - 4 = 3 + 8x

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

20.

Solve the equation
4x - 5x + 9 =5x - 9

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

21.

14p - 8 = 22 + 20p

a)

-5

b)

5

c)

30

d)

-30

22.

The goal of solving a one, two, or multi-step equations is to:

a)

Find the constant

b)

Find the coefficient

c)

Find the value of the variable

d)

Be confused

23.

2x = x + 3

a)

6

b)

3

c)

2

d)

x

24.

7x = 3x + 24

a)

6

b)

10

c)

14

d)

4

25.

30 + 6t = 11t

a)

3

b)

5

c)

6

d)

30

26.

5 - 2t = 3t

a)

1

b)

5

c)

3

d)

2

27.

6z = 49 - z

a)

49

b)

-7

c)

6

d)

7

28.

n - 1 = -11

a)

5

b)

10

c)

-10

d)

-11

29.

a)

x = 1

b)

x = 2

c)

x = 1/2

d)

x = 3/2

30.

Solve for a:

9+2a = -3-4a

a)

a=5

b)

a= -1

c)

a= -2

d)

a=2

31.

2x = x + 3

a)

6

b)

3

c)

2

d)

x

32.

30 + 6t = 11t

a)

3

b)

5

c)

6

d)

30

33.

10x + 9 = 4x - 9

a)

0

b)

3

c)

-3

d)

-18

34.

8x - 8 = -4x + 16

a)

8

b)

16

c)

24

d)

2

35.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

36.

Solve the equation
4x - 5x + 9 =5x - 9

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

37.

Solve:
5y+34 = -2(-7y+1)

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

38.

Solve: 2(4x - 3) - 8 = 4 + 2x

a)

5/3

b)

3

c)

1

d)

2

39.

-(8n - 2) = 3 + 10(1 - 3n)

a)

n = 1/2

b)

n = -1/2

c)

n = 2

40.

Solve
1/2(s-12)= 1/4(s+ 16)

a)

s = -40

b)

s= 40

c)

s=20

d)

s= -20

41.

Write the equation for the model.

a)

2x - 2 = -x - 8

b)

-x - 2x = 2x - 8x

c)

-x - 2 = 2x - 8

42.

Solve the equation.

a)

x=-5

b)

x=-17

c)

x=5

d)

x=17

43.

a)

-x - 4 = 2x + 2

b)

-x - 2 = 2x - 4

c)

-x + 2 = 2x - 4

44.

Solve the equation.

a)

x=-5

b)

x=-1

c)

x=-15

d)

x=-3

45.

Write the equation for the model.

a)

5x + 5 = 3x + 1

b)

5x - 1 = 3x + 5

c)

5x + 1 = 3x + 5

46.

Write the equation for the model.

a)

-x + 2 = 2x - 1

b)

-x + 2x = 2x - x

c)

2x + 2 = -x - 1

47.

Write the equation for the model.

a)

2x - 2 = -x + 7

b)

2x + 2 = x + 7

c)

2x + 7 = -x - 2

48.

Solve the equation.

a)

x = 4

b)

x = 8

c)

x = 12

d)

x = 3

49.

The equation for the model is 3x - 5 = 7. What is the value of x?

a)

x = 6

b)

x = 4

c)

x = 7

d)

x = 12

50.

Write the equation for the model.

a)

-x - 4 = 3x

b)

3x + 4 = -x

c)

3x - 4 = -x

51.

a)

x = 4

b)

x = -4

c)

x = 36

d)

x = -36

52.

Write the equation for the model.

a)

3x + 1 = -x + 5

b)

-x + 1 = 3x + 5

c)

-x + x = 3x + 5x

53.

Write the equation for the model.

a)

-2x - 1 = 2x - 9

b)

2x - 1 = -2x - 9

c)

-2x - 9 = 2x - 1

54.

Write the equation for the model.

a)

3x + 8 = x

b)

3x = x + 8x

c)

3x = x + 8

55.

Write the equation for the model.

a)

3x + x = -x - 3x

b)

-x + 1 = 3x - 3

c)

3x + 1 = -x - 3

56.

Write the equation for the model.

a)

2x - 4 = x - 7

b)

2x + 4 = x + 7

c)

x - 4 = 2x - 7

57.

Write the equation for the model.

a)

3x - 7x = 2x + 5x

b)

3x + 5 = 2x - 7

c)

3x - 7 = 2x + 5

58.

Write the equation for the model.

a)

2x + 7 = -3x + 2

b)

2x - 2 = 3x - 7

c)

2x + 2 = -3x + 7

59.

Write the equation for the model.

a)

2x + 3 = x + 1

b)

2x + 1 = x + 3

c)

2x - 1 = x - 3

60.

Write the equation for the model.

a)

3n - 6 = -n + 4

b)

3n + 4 = -n - 6

c)

3n + 4n = -n - 6n

61.

Write the equation for the model.

a)

3x + x = -x - 3x

b)

-x + 1 = 3x - 3

c)

3x + 1 = -x - 3

62.

Write the equation for the model.

a)

2x + 7 = -3x + 2

b)

2x - 2 = 3x - 7

c)

2x + 2 = -3x + 7

63.

a)

x = 10

b)

x = 5

c)

x = 3

d)

x = -3

64.

a)

x = 10

b)

x = 9

c)

x = -10

d)

x = -9

65.

Solve:
10x + 9 = 4x - 9

a)

0

b)

3

c)

-3

d)

-18

66.

Solve:

8x - 8 = -4x + 16

a)

x = 8

b)

x = 16

c)

x = 24

d)

x = 2

67.

Solve:

a)

x = 13

b)

x = -13

c)

x = 12

d)

x = -15

68.

Solve:

$-3+2a=9-4a$

(Enter ONLY the number)

(a)

69.

Solve:

$2x+4=10+5x$

(Enter ONLY the number)

(a)

70.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. Which equation could you use to see when the two companies would charge the same amount?

a)

18x = 22x

b)

3x + 15 = x + 21

c)

15x + 3 = 21x + 1

d)

3x + 15 + 21x = 1

71.

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

a)

15x + 2.5 = 10x + 3

b)

15 - 2.5x = 10 - 3x

c)

15 + 2.5x = 10 + 3x

d)

15 - 10 = 2.5x + 3x

72.

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

a)

150x + 24 = 180 + 20x

b)

150 + 24x = 180 + 20x

c)

180 - 150 = 24 x + 20x

d)

150 - 24x = 180 - 20x

73.

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same. (Use an equation to help solve the problem)

a)

3 hours

b)

4 hours

c)

1 hour

d)

2 hours

74.

Juan decided to join a gym to get in shape for football. He has two payment options. Option A is to buy a membership card and pay $2 each time he goes to the gym. Option B is to pay $4 each time he goes. A membership card costs $30. After how many times, t, will the cost of Option A be equal to the cost of Option B

a)

50

b)

20

c)

15

d)

25

75.

Select the situation that could be modeled by: 8 + 4x = 12 + 3x.

a)

Winnie bought a family meal with 8 burgers and 4 fries. Wilson bought a family meal with 12 burgers and 3 fries. If they each paid the same amount, how much did they spend?

b)

Team A runs 8 drills that a 4 minutes each. Team B runs 12 drills that are 3 minutes each. Which team practices longer?

c)

The basketball team currently has 8 players and is growing by 4 players each month. The volleyball team has 12 players and is growing by 3 players each month. After how many months will they have the same number of players?

76.

7x = 3x + 24

a)

6

b)

10

c)

14

d)

4

77.

-8y = -3y -15

a)

3

b)

-3

c)

5

d)

-5

78.

8w - 8 = -4x + 16

a)

8

b)

16

c)

24

d)

2

79.

7w + 5 = 3w - 15

a)

5

b)

-2

c)

2

d)

-5

80.

Solve for x:
4(1 - x) + 3x = - 2(x + 1)

a)

x = -6

b)

x = 6

c)

x = 3

81.

Solve:
2(4x - 3) - 8 = 4 + 2x

a)

x = 5/3

b)

x = 3

c)

x = 1

d)

x = 2

82.

Solve:
5y + 34 = -2(- 7y + 1)

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

83.

Solve the equation
12x - 15 = 3(2x + 3)

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

84.

Solve the equation.

a)

x=-5

b)

x=-17

c)

x=5

d)

x=17

85.

Solve the equation.

a)

x=-5

b)

x=-1

c)

x=-15

d)

x=-3

86.

Using the model, write the equation and solve.

a)

6 = 2x; x = 4

b)

6 = 2x; x = 8

c)

6 = 2x; x = 12

d)

6 = 2x; x = 3

87.

What is represent by the model?

a)

2b+8-12

b)

2b+8=12

c)

8-2b=12

d)

b²+8=12

88.

a)

x = 4

b)

x = -4

c)

x = 36

d)

x = -36

89.

a)

x = 2

b)

x = -12

c)

x = -2

d)

x = 12

90.

7x = 5x - 12

a)

8

b)

-1

c)

1

d)

-6

91.

Solve. Use a T-chart.
6(4x+2)= 3(8x+4)

a)

Identity

b)

No Solution

c)

12

d)

6

92.

The equation for the model is 3x - 5 = 7. What is the value of x?

a)

x = 6

b)

x = 4

c)

x = 7

d)

x = 12

93.

Solve the equation
4x - 5x + 9 =5x - 9

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

94.

The goal of solving a one, two, or multi-step equations is to:

a)

Find the constant

b)

Find the coefficient

c)

Find the value of the variable

d)

Be confused

95.

2(x + 6) + 3 = 9 + 5x

a)

16

b)

2

c)

-8

d)

-10

96.

Which statement best describes the first step to the equation?

-11-3x=44-2x

a)

Add 3 to both sides

b)

Add 11 to both sides

c)

Get the variables on one side

d)

Add 2 to both sides

97.

Inverse of
multiplication

a)

division

b)

subtraction

c)

multiplication

d)

equals

98.

Inverse of
substraction

a)

multiplication

b)

addition

c)

division

d)

equal

99.

Inverse of
addition

a)

division

b)

multiplication

c)

subtraction

d)

equals

100.

Inverse of
division

a)

addition

b)

equals

c)

subtraction

d)

multiplication

101.

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

a)

15x + 2.5 = 10x + 3

b)

15 + 2.5x = 10 + 3x

c)

15 - 2.5x = 10

d)

15 - 10 = 2.5x + 3x

102.

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

a)

150x + 24 = 180 + 20x

b)

180 - 150 = 24 x + 20x

c)

150 + 24x = 180 + 20x

d)

150 - 24x = 180 - 20x

103.

Select the situation that could be modeled by: 120 + 25x = 45x.

a)

John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?

b)

George charges a flat fee of $120 to mow a lawn plus $25 an hour. Greg charges $45 a hour to mow a lawn. After how many hours do they make the same amount?

c)

Lisa pays $120 for each purse she buys plus an additional $25 to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

104.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. Write an equation to show when the amount of hours the total fee charged by the companies the same?

a)

15x + 3 = 21x + 1

b)

15 + 3x = 21 +x

c)

15 - 3x = 21 - 1x

d)

15 + x = 21 + 3x

105.

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Set up an equation to find the number of hours for which the total amount that both places charge would be the same.

a)

20x - 14x = 4

b)

20 - 4x = 14x

c)

20x + 4 = 14x

d)

20 + 4x = 14x

106.

Taxi company A charges $8.00 to get into the cab and $0.75 per mile. Taxi company B charges $6.00 to get into a cab and $1.25 per mile. Write an equation to show when the number of miles would cost the same for both companies?

a)

8x + 0.75 = 6x + 1.25

b)

8 + 0.75x = 6 + 1.25x

c)

8 + 6 = .75x + 1.25x

d)

8 - .75x = 6 - 1.25x

107.

WRITE AN EQUATION TO REPRESENT THE SITUATION

Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day.

a)

400 - 75x = 1,000 + 25x

b)

400 + 75x = 1,000 – 25x

c)

400x - 75 = 1,000x + 25

d)

400x + 75 = 1,000x – 25

108.

WRITE AN EQUATION TO REPRESENT THE SITUATION

Peter and his friends are going to play putt-putt. At one location, they can pay $2.00 for rentals plus $7.50 per game. At another location, it would cost $8.00 for rentals plus $6.00 per game.

a)

2 + 7.50x = 8 + 6x

b)

2 - 7.50x = 8 - 6x

c)

2x + 7.50 = 8x + 6

d)

2x - 7.50x = 8 x- 6

109.

WRITE AN EQUATION TO REPRESENT THE SITUATION

Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week.

a)

155x - 10 = 230x + 15

b)

155x + 10 = 230x – 15

c)

155 - 10x = 230 + 15x

d)

155 + 10x = 230 – 15x

110.

WRITE AN EQUATION TO REPRESENT THE SITUATION

Kimberly takes the bus to work. The bus ride to work costs her $2.50 each time. She could buy a bus pass for a one-time fee of $15.00 and would then only pay $1.00 each time to ride the bus.

a)

2.50 + x = 15x

b)

2.50x = 15x + 1

c)

2.50x = 15 + x

d)

2.50x = 15x

111.

Cheryl has saved $145 towards a vacation. She earns $6 an hour working as a cashier. Mike has $80 saved towards his vacation and earns $7 an hour as a waiter. How many hours will they have to work so they have the same amount of money saved?

a)

145 + 6x = 80 + 7x

b)

145x + 6 = 80x + 7

c)

145 - 6x = 80 - 7x

d)

145 + 7x = 80 + 6x

112.

A new rose bush is 5 inches tall and grows 9 inches each year. A sunflower from a seed grows 6.5 inches per year. When will they be the same size?

a)

9x + 5 = 6.5x

b)

9 + 5x = 6.5x

c)

9 - 5x = 6.5x

d)

9x - 5 = 6.5x

113.

"Increased by" is a key phrase for...

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

114.

"Each" is a key phrase for...

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

115.

"Fewer" is a key phrase for...

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

116.

A fraction with 1 is the numerator is the same as...

a)

Addition

b)

Mulitplication

c)

Subtraction

d)

Division

117.

Write an equation for #4 on your foldable.

a)

-155 - 10x = 230 - 15x

b)

155 +10x = 230 - 15x

c)

155 + 230 = 10x + 15x

d)

155 + 15x = 230 - 10x

118.

Solve #4 on your foldable.

a)

-17

b)

3

c)

5

d)

6

119.

Write the equation for #5 on your foldable.

a)

2.5x + 1 = 15

b)

1x + 2.5x = 15

c)

2.5x = 15 +1x

120.

Solve #5 on your foldable.

a)

10

b)

12

c)

13

d)

9

121.

Write an equation for #6 on your foldable.

a)

-7x + 35 = 0.8x + 43

b)

5x + 6 = 12x +10

c)

x - 2= 5x +3

d)

0.8x + 35 = -7x - 43

122.

solve #6 on your foldable.

a)

10

b)

-10

c)

9

d)

6

123.

Combine like terms: 4x -2 + 3x -4

a)

1x + 2

b)

7x + 6

c)

7x -6

d)

8x - 3

124.

Combine like terms: -4x + 4 -2x -3

a)

2x - 1

b)

-5x - 1

c)

2x + 1

d)

-6x + 1

125.

What is a key word for the following symbol?

<

a)

Fewer Than

b)

More Than

c)

Less Than or Equal To

d)

Greater Than or Equal To

126.

What is a key word for the following symbol?

>

a)

At most

b)

At least

c)

Above

d)

Below

127.

Joe’s Catering Company charges a $45 set-up fee plus $12.50 per person. Jimmy’s catering company charges a $75 set up fee plus $7.50 per person. Which inequality could be used to determine x, the number of people for which Joe’s Catering Company would be less expensive than Jimmy’s catering company?

a)

45 + 12.5x > 75 + 7.5x

b)

45 + 12.5x ≥ 75 + 7.5x

c)

45 + 12.5x < 75 + 7.5x

d)

45 + 12.5x ≤ 75 + 7.5x

128.

Norah has never lost a tooth, but she will receive $0.75 from the tooth fairy each time she loses a tooth. Kate has $1.25 from the tooth fairy, and she gets $0.25 each time she loses a tooth. Which inequality could be used to find x, the number of teeth that each girl would have to lose for Norah to have at least as much money from the tooth fairy as Kate?

a)

0.75x ≥ 1.25 + 0.25x

b)

0.75x ≥ 1.25 – 0.25x

c)

0.75x ≤ 1.25 + 0.25x

d)

0.75x > 1.25 + 0.25x

129.

An inequality is the relation between two expressions that are ____________________________to one another.

a)

equal

b)

not equal

130.

Write an inequality to represent the following relationship:
Three times a number minus two is less than the number plus ten.

a)

3x - 2 < x + 10

b)

2 - 3x < x + 10

c)

3x - 2 > x + 10

d)

2 - 3x > x + 10

131.

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

a)

80+9.50x > 120+7.50x

b)

80+9.50x < 120+7.50x

c)

80x+9.50 > 120x+7.50

d)

80x+9.50 < 120x+7.50

132.

What inequality symbol is used in:
384 + 2x < 6x?

a)

Greater Than

b)

Less Than

c)

Greater Than or Equal To

d)

Less Than or Equal To

133.

Choose the best inequality for the situation.

a)

25 + 8x = 12x

b)

12x < 25 + 8x

c)

25 + 12x < 8x

d)

25 + 8x ≤ 12x

134.

Which inequality represents after what time it will take Adele's swimming pool to have more water than Pink's?

a)

180 + 8x < 6x

b)

180 − 8x ≥ 6x

c)

6x = 180 − 8x

d)

6x > 180 − 8x

135.

The temperature in the ice rink must stay below 50°F. This morning, the temperature was 71°F. The ice rink runs a cooling device that can decrease the temperature by 3.5° every hour. Which inequality shows how long it will take for the temperature to fall below 50°F?

a)

50 + 3.5x < 71

b)

71 - 3.5x < 50

c)

71 - 3.5x ≤ 50

d)

71 + 3.5x < 50

136.

The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?

a)

106 - 4x ≤ 70

b)

70 + 4x ≤ 106

c)

4x - 106 ≥ 70

d)

106 - 4x< 70

Equations and Inequalities with Variables on Both Sides

Total questions: 136

Worksheet time: 13hrs 57mins

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