Free Printable Simplifying Expressions & Solving Equations

1.

-6x = 30

a)

x = - 5

b)

x = 24

c)

x = 5

d)

x = 36

2.

$\frac{t}{-8}=\ -5$

a)

t = 3

b)

t = -40

c)

t = -3

d)

t = 40

3.

Which choice models this situation? William needs to sell 25 Husky Cards for a fundraiser by Friday. So far, he has sold 9 cards. How many tickets does he still need to sell?

a)

t - 9 = 25

b)

t + 9 = 25

c)

9t = 25

d)

t/9 = 25

4.

Which choice models this situation?

Last week, James worked 35 hours in 5 days on the farm. He worked the same number of hours each day. How many hours did he work each day?

a)

h - 5 = 35

b)

h + 5 = 35

c)

5h = 35

d)

h/5 = 35

5.

Which choice models this situation?

At ACHI, there are 5 art classes with 24 students per class. How many students altogether are in the art classes?

a)

s - 5 = 24

b)

s + 5 = 24

c)

5s = 24

d)

s/5 = 24

6.

Which choice models this situation?

Hadlee needed new pencils for school today. She took 6 pencils from a new box of pencils. If there are 18 pencils left in the box, how many pencils were in the brand new box?

a)

p - 6 = 18

b)

p + 6 = 18

c)

6p = 18

d)

p/6 = 18

7.

Which choice models this situation?

Maddi participated in a read-a-thon. Mrs. Dunnmeyer pledged $4 for each book read. When it ended, she gave Maddi a total of $44. How many books did Maddi read?

a)

b - 4 = 44

b)

b + 4 = 33

c)

4b = 44

d)

b/4 = 44

8.

Solve the following equation

j - (-5) = 15

a)

j = 20

b)

j = 3

c)

j = 75

d)

j = 10

9.

Solve the following equation

2y = 18

a)

y = 36

b)

y = 16

c)

y = 9

d)

y = 20

10.

Brooklyn is preparing for her younger sister's birthday party. She splits a jar of lollipops evenly among 6 goody bags. The goody bags ends up with 4 lollipops per bag.

Which equation can you use to find the number of lollipops n in the jar?

a)

n/6 = 4

b)

n - 4 = 6

c)

4n = 6

d)

n + 6 = 4

11.

Find the value of the variable: m + 4 = 12

a)

16

b)

8

c)

48

d)

3

12.

Find the value of the variable: m - 4 = 12

a)

16

b)

8

c)

48

d)

3

13.

Find the value of m: $\frac{m}{5}\ =\ 10$

a)

2

b)

5

c)

50

14.

Find the value of m: 5m = 10

a)

50

b)

2

c)

5

15.

What is the inverse of addition?

a)

multiplication

b)

division

c)

subtraction

d)

addition

16.

What is the inverse of multiplication?

a)

Addition

b)

Subtraction

c)

Division

17.

5 + c = 8

a)

3

b)

13

c)

5

d)

8

18.

c - 5 = 8

a)

3

b)

13

c)

5

d)

8

19.

What is the inverse of division?

a)

Addition

b)

Multiplication

c)

Subtraction

20.

What is the inverse of subtraction?

a)

Division

b)

Multiplication

c)

Addition

21.

Find the value of a: 12 = 4a

a)

48

b)

3

c)

8

22.

Find the value of a: $12\ =\ \frac{a}{4}$

a)

48

b)

3

c)

8

23.

Find the value of the variable: $\frac{1}{2}x\ =\ 10$

a)

5

b)

20

c)

4

24.

Find the value of the variable: k - 2.14 = 85

a)

82.86

b)

2.99

c)

87.14

25.

$Find\ the\ value\ of\ the\ variable:\ \ 8\ =\frac{k}{2.5}$

a)

5

b)

10

c)

20

26.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

27.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

28.

Figure out what n equals in this equation:
6n + 4 = -26

a)

n=-6

b)

n= -5

c)

n= 8

d)

n= -4

29.

In the equation 4y - 9 = -36
y = -4

a)

True

b)

False

30.

5x + 4 = −6

a)

2

b)

-2

c)

10

d)

15

31.

-4x + 1 = 21

a)

x=120

b)

x=5

c)

x=30

d)

x=-5

32.

x - 4 = 12

a)

x = 8

b)

x = 16

c)

x = -8

d)

x = 3

33.

2x + 6 = 14

a)

x = 4

b)

x = 10

c)

x = -4

d)

x = 3

34.

-3x + 5 = -13

a)

x = -5

b)

x = 2

c)

x = -6

d)

x = 6

35.

x / 2 - 5 = 3

a)

x = -2

b)

x = 2

c)

x = 16

d)

x = 8

36.

6p - 5 =13

a)

12

b)

15

c)

3

d)

-3

37.

Solve for x:
-30 - 5x = 120

a)

x = 18

b)

x = -18

c)

x = 30

d)

x = -30

38.

15 = 2a + 7

a)

2

b)

4

c)

12

d)

14

39.

Solve for w:
-6w + 1 = -11

a)

2

b)

1.2

c)

12

d)

-2

40.

x/5 - 13 = 20

a)

145

b)

165

c)

180

d)

190

41.

4x + 22 = -34

a)

-14

b)

-22

c)

16

d)

-20

42.

Solve -5t + 9 = 24

a)

-3

b)

3

c)

12

43.

WRITE AN EQUATION
You bought a $5 magazine and four
erasers. You spent a total of $25. How
much did each eraser cost?

a)

5+x=25

b)

5+4x=25

c)

5x=25

d)

23-5=4x

44.

4x + 7 = 23

a)

x = 16

b)

x = 4

c)

x = 9

d)

x = 12

45.

WRITE AN EQUATION
331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

a)

331=7x+6

b)

331=13x

c)

331=6x+7

d)

331-7=6x

46.

4x + 7 = 23

a)

x = 16

b)

x = 4

c)

x = 9

d)

x = 12

47.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

48.

20 = 2 - a

a)

a= 18

b)

a= -18

c)

a= -10

d)

a= 12

49.

7 + ^a⁄₃= 5

a)

a= -2

b)

a= -6

c)

a= 3

d)

a= 15

50.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

51.

-4x+1=21

a)

x=120

b)

x=5

c)

x=30

d)

x=-5

52.

The steps in solving 5b - 6 = 24 are:

a)

Add 6 to both sides and divide both sides by 5

b)

Add 6 to both sides and multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

53.

Solve the equation for x:
2x + 3x + 4 = 44

a)

x = 8

b)

x = 9

c)

x = 10

d)

x = 11

54.

Solve the equation for x:
8x - 6x + 4 + 5 = 19

a)

x = 4

b)

x = 5

c)

x = 6

d)

x = 7

55.

3(3x - 6) = 18

a)

x = 4

b)

x = -4

c)

x=8

d)

x= -12

56.

-11 + 3(b + 5) = 7

a)

b = 1

b)

b= -1

c)

b = 3

d)

b = -3

57.

a)

x= 9

b)

x= -9

c)

x= 11

d)

x= -11

58.

Solve for x.
4(2x+8)-3x = 47

a)

13

b)

2

c)

3

d)

7.8

59.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

60.

^x/₄- 3 = 9

a)

48

b)

24

c)

3

d)

36

61.

5n + 11n

a)

16n

b)

55n

c)

6n

62.

5(a + 6)

a)

5a + 6

b)

a + 30

c)

5a + 30

d)

5a - 30

63.

3(2c - 5)

a)

6c - 15

b)

6c + 15

c)

6c + 15

d)

-6c - 15

64.

A letter that represents a number is called a _____.

a)

variable

b)

coefficient

c)

constant

d)

term

65.

A number with no variable attached is called a _____.

a)

coefficient

b)

constant

c)

variable

d)

term

66.

Simplify the following expression:
-10x + 15 - 3x + 2

a)

13x² + 17

b)

-13x² + 13

c)

-13x + 17

d)

-7x + 17

67.

Simplify:
1y + 2x + 3y + 4x

a)

1y + 6x + 3y

b)

-4y + 6x

c)

4y + 6x

d)

4x + 6y

68.

Simplify the following expression:
19 - ( 3 - 5b)

a)

16 + 5b

b)

21 + 5b

c)

16 - 5b

d)

21 - 5b

69.

Simplify ¹/₂x + ¹/₄x + 5 - 3

a)

¹/₃x + 2

b)

³/₄x + 2

c)

¹/₄x - 2

d)

³/₄x - 2

70.

Simplify: 0.5y + 2.3y -8 - 2

a)

7.3y - 6

b)

2.8y - 6

c)

1.8y -10

d)

2.8y -10

71.

Find the missing number using the distributive property.
10 + 20 = 2(5 + __)

a)

2

b)

4

c)

5

d)

10

72.

Which of the following is equivalent to 8h +7(2 + 4h)?

a)

90h

b)

12h + 14

c)

50h

d)

36h +14

73.

Which of the following is equivalent to 8(5f - 7) + 3f ?

a)

43f - 7

b)

-13f

c)

43f - 56

d)

40f -7 + 3f

74.

2r - 2(7r + 8) + -4

a)

-16r + 12

b)

-12r + 8

c)

-16r + 4

d)

-12r - 20

75.

3(9a + 2) + 5(2a - 4)

a)

37a + 6

b)

37a + 26

c)

11a + 6

d)

37a - 14

76.

Which answer choice contains ALL like terms?

a)

-4x, 2x, 3x

b)

-4x, 2, 3y

c)

4x², 2x

d)

14, 4x

77.

In the expression below, the 3 is known as the _________________________

3y

a)

coefficient

b)

variable

c)

constant term

78.

What is the coefficient in the following expression?
5x - 9

a)

-9

b)

5

c)

x

d)

5x

79.

Simplify the Expression.
9z - 21 - 3z + 10

a)

Simplified

b)

9z - 21 - 7

c)

9z - 11 -3z

d)

6z - 11

80.

4a + 9 + a

a)

5a + 9

b)

14a

c)

3a + 9

d)

5a - 9

81.

Simplify 5(2 - 7n)

a)

52 - 57n

b)

10 - 7n

c)

10 - 35n

d)

10 + 35n

82.

a)

35x+7

b)

35x-1

c)

35x-7

d)

-35x-7

83.

Simplify the expression.

11\left(b-3\right)

a)

$11b-33$

b)

$8b$

c)

$11b-3$

d)

$33b$

84.

-8(3 + 4w)

a)

-5 + -4w

b)

-24 - 4w

c)

-24 + -32w

d)

-11 + -12w

85.

-9(-3 + 5v)

a)

-7 + 49v

b)

27 - 45v

c)

8 - 80v

d)

3 - 80v

86.

-2(3y - 5)

a)

-6y + 10

b)

-23y - 5

c)

-5y - 7

d)

-6y - 10

87.

Simplify:
1y - 2x - 3y + 4x

a)

-2x + 2x

b)

-2y - 2x

c)

-4y - 6x

d)

2y - 2x

88.

Simplify:
13y + (-4) + 7

a)

13y + 3

b)

13y - 3

c)

16y

d)

-13 + 3

89.

Simplify 5(2 - 7n)

a)

52 - 57n

b)

10 - 7n

c)

10 - 35n

d)

10 + 35n

90.

Simplify 6(x + -2)

a)

6x + -2

b)

6x + -12

c)

4x

d)

6x - 2

91.

Simplify:

5x - 6x - 8x + 7

a)

-9x + 7

b)

10x + 7

c)

9x + 7

d)

9x - 7

92.

4a + 9 + a

a)

5a + 9

b)

14a

c)

3a + 9

d)

5a - 9

93.

Simplify:
20x + 27y + 38y + 29x

a)

49y + 64x

b)

49y + 65x

c)

49x + 65y

d)

49x - 65y

94.

Use the distributive property to simplify the expression.

3(2c - 5)

a)

6c - 15

b)

6c + 15

c)

6c + 15

d)

-6c - 15

95.

Use the distributive property to simplify the expression.

9(2g + 3)

a)

18g + 27

b)

18g - 27

c)

-18g - 27

d)

18g - 18

96.

-7(w-4)+3w - 27

a)

10w + 21

b)

-4w + 1

c)

3w + 5

d)

2w - 5

97.

4(x+3) - 5

a)

4x + 7

b)

4x - 2

c)

4x - 17

d)

4x + 2

98.

6(7 + x) + 5x

a)

6x + 13

b)

x + 42

c)

6x + 42

d)

11x + 42

99.

3(5 + 3x) - 4x

a)

-x + 8

b)

7x + 15

c)

5x + 15

d)

7x + 8

100.

5(y + 6) + 4

a)

5y + 15

b)

5y + 34

c)

5y + 10

d)

y + 34

101.

6(3x - 2) + 4x

a)

22x - 12

b)

7x + 4

c)

22x - 2

d)

18x + 2

102.

3(2 + x) + 6x - 4

a)

6x + 5

b)

9x + 1

c)

9x + 2

d)

3x + 8

103.

x + 2(x + 3)

a)

3x + 5

b)

3x + 6

c)

2x + 8

d)

3x - 6

104.

5(1 - y) - 3y

a)

-4y + 5

b)

-2y + 5

c)

3y + 5

d)

-8y + 5

105.

1 + (a + 3)3

a)

a + 12

b)

3a + 4

c)

3a + 10

d)

a + 9

106.

-5(y - 6) + 4

a)

-5y + 34

b)

5y - 26

c)

-5y - 26

d)

5y + 34

107.

6(-x - 2) - 4x

a)

2x - 12

b)

10x - 12

c)

-2x + 12

d)

-10x - 12

108.

6x + 3(-2 - x) - 4

a)

9x - 10

b)

3x + 2

c)

3x - 10

d)

9x + 10

109.

2x = x + 3

a)

6

b)

3

c)

2

d)

x

110.

30 + 6t = 11t

a)

3

b)

5

c)

6

d)

30

111.

10x + 9 = 4x - 9

a)

0

b)

3

c)

-3

d)

-18

112.

8x - 8 = -4x + 16

a)

8

b)

16

c)

24

d)

2

113.

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

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

114.

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

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

115.

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

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

116.

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

a)

5/3

b)

3

c)

1

d)

2

117.

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

a)

n = 1/2

b)

n = -1/2

c)

n = 2

118.

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

a)

s = -40

b)

s= 40

c)

s=20

d)

s= -20

119.

What is the first step to solve this equation:

11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

120.

What is the first step you should take to solve this problem?

1 + 4n - 6n = 1 - 8n

a)

subtract 8n to both sides

b)

multiply 6n to both sides

c)

combine the like terms 4n + -6n

121.

What is the next step you should take?

1 + 4n = 10 - 14n

a)

Collect the variables (letters) to the left

b)

add 1 from both sides

c)

subtract 14n to both sides

122.

What is the next step you should take?

1 + 18n = 33

a)

subtract 1 to both sides

b)

collect the numbers to the right

c)

add 1 to both sides

d)

multiply 18 to both sides

123.

What is the final answer to

10 + 2n = 8n - 2n + 10 ?

a)

12

b)

5

c)

0

d)

-15

124.

What is the first step you should take to solve this problem?

-3(x - 2) = -8 +9b

a)

add 8 to both sides

b)

subtract 9b from both sides

c)

Distribute -3 to the x and -2

125.

What is the next step you should take?

14x + 8 = -3 - 7x

a)

Collect the variables (letters) on the left side

b)

multiply -7 to both sides

c)

add 14x to both sides

d)

subtract 7x to both sides

126.

What is the next step you should take?

-11b + 8 = -3

a)

subtract 8 from both sides

b)

add -3 to both sides

c)

divide 8 to both sides

d)

multiply 3 to both sides

127.

What is the next step you should take?

-11x = -11

a)

add 11 to both sides

b)

subtract 11 from both sides

c)

divide both sides by 11

d)

divide both sides by -11

128.

What is the final answer to

4(x - 2) = -3 + 5x

a)

2

b)

-10

c)

-5

d)

-3

129.

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

a)

Subtracted 2x from both sides of the equation

b)

Subtracted 9 from both sides of the equation

c)

Multiplied both sides of the equation by 3

d)

Added -3 to both sides of the equation

130.

Mrs. Bautch wants to wish you a Merry Christmas.

a)

True

b)

False

131.

Solve for x:

2x - 5 = 3x + 4

a)

x = 6

b)

x = -9

c)

x = -18/13

d)

x = 10/3

132.

5w + 5 = 8w - 10

a)

-5

b)

-2

c)

2

d)

5

133.

Solve the equation

4x - 5x + 9 =5x - 9

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

134.

8x - 8 = -4x + 16

a)

8

b)

16

c)

24

d)

2

135.

24 = 2a - 6

a)

a=-15

b)

a=15

c)

a= 9

d)

a= -9

136.

2 + (¹∕₄)a = 10

a)

a= 32

b)

a= 48

c)

a= 2

d)

a= -2

137.

3 + ^a⁄₃= 6

a)

a= 1

b)

a= 3

c)

a= 9

d)

a= 15

138.

50 = 28.1 + 0.15a

a)

a= 150

b)

a= 146

c)

a= 6

d)

a= 155

139.

10x + 9 = 4x - 9

a)

0

b)

3

c)

-3

d)

-18

140.

7w + 5 = 3w - 15

a)

5

b)

-2

c)

2

d)

-5

141.

8w - 8 = -4x + 16

a)

8

b)

16

c)

24

d)

2

142.

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

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

143.

Solve: 5x - 14 = 8x + 4

a)

6

b)

-6

c)

-18/13

d)

10/3

144.

2c - 12 = 9c + 2

a)

14

b)

2

c)

-2

145.

f - 4 = 6f + 26

a)

-5

b)

5

c)

6

d)

-6

146.

14p - 8 = 22 + 20p

a)

-5

b)

5

c)

30

147.

12x - 15 = 3(2x+3)

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

148.

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

a)

16

b)

2

c)

-8

d)

-10

149.

-6(1 - 6r) = -2(r + 3)

a)

14

b)

0

c)

-11

d)

4

150.

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

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

151.

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

a)

5/3

b)

3

c)

1

d)

2

152.

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

a)

y = -4

b)

y = 9

c)

y = 4

d)

y = 36/19

153.

8 - 9t = 21t - 17

a)

t = 6/5

b)

t = 5/6

c)

t = 1

154.

3 - 5x = -9 + x

a)

4

b)

3

c)

2

d)

1

Simplifying Expressions & Solving Equations

Total questions: 154

Worksheet time: 8hrs 42mins

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