Free Printable Chapter 6:Solving Equations

1.

Translate the following sentence into an equation:

The sum of twice a number x and 13 is two less than 3 times x.

a)

2 (x + 13) + 3x - 2

b)

2x + 13 = 2 - 3x

c)

2x + 13 = 3x - 2

d)

2x + 13 = 3 (x - 2)

2.

The difference of a number x and 2 is 7.

a)

x - 2 = 7

b)

x + 2 = 7

c)

2x = 7

d)

2/x = 7

3.

7 times a number a is 42.

a)

7a = 42

b)

7 + a = 42

c)

7/a = 42

d)

7 - a = 42

4.

To solve the equation below, you would:
x - 62 = 123

a)

add 62 to each side

b)

subtract 62 from each side

c)

multiply each side by 62

d)

Add 123 to each side

5.

The objective when solving an equation is to....

a)

isolate the variable.

b)

check the solution.

c)

guess and check.

d)

Combine Like Terms.

6.

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.

7.

What is the second step in solving the following equation?
-3x + 5 = 20

a)

Subtract 5 from both sides

b)

Divide both sides by -3

c)

Divide both sides by 3

d)

add 3x to both sides

8.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

9.

What inequality does the number line graph represent?

a)

x ≥ 3

b)

x > 3

c)

x < -3

d)

x ≤ 3

10.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

11.

4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

12.

7b - 3 < 11

a)

b < 2

b)

84 > b

c)

b > 2

d)

b < 84

13.

Which of the following is a solution to the inequality?

m < 25

a)

m = 30

b)

m = 25

c)

m = 21

d)

m = 27

14.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

15.

2v + 7 = 3

a)

v = -4

b)

v = -2

c)

v = 3

d)

v = 5

16.

4b + 3 = −9

a)

b = -3

b)

b = -6

c)

b = 2/3

d)

b = 4

17.

17 = 5k − 2

a)

k = 3

b)

k = 4 2/5

c)

k = 2 1/5

d)

k = 3 4/5

18.

−6t − 7 = 17

a)

t = -6

b)

t = -2

c)

t = -4

d)

t = 6

19.

−4p + 9 = −5

a)

p = 3.5

b)

p = 4.5

c)

p = 4

d)

p = -5

20.

11 = −5x − 2

a)

x = -2.9

b)

x = -2.3

c)

x = 13

d)

x = -2.6

21.

-3(2c - 5) = 15

a)

-5

b)

5

c)

0

d)

6

22.

2x + 4 + 5x = 13 + 4x

a)

-3

b)

9

c)

3

d)

1

23.

3x - 4(2 + 3x) = 82

a)

no solution

b)

-10

c)

6

d)

18

24.

2x - (3 + 4x) = 11

a)

-4

b)

7/3

c)

-7

d)

-17/8

25.

7(2x - 4) = 42

a)

x= 5

b)

x= 8

c)

x= 2

d)

x= 9

26.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

27.

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

a)

4

b)

3

c)

2

d)

1

28.

38 + 7k = 8(k + 4)

a)

6

b)

8

c)

-6

d)

1

29.

Solve for x:

4(1 - x) + 3x = -2(x + 1)

a)

x = -6

b)

x = 6

c)

x = 3

30.

Solve:

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

a)

x = 5/3

b)

x = 3

c)

x = 1

d)

x = 2

31.

Solve the equation

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

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

32.

Solve the equation

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

a)

x = -8

b)

x = 8

c)

x = 2

d)

x = -2

33.

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

a)

n = 1/2

b)

n = -1/2

c)

n = 2

34.

12x = 144

a)

x = 12

b)

x = 4

c)

x = 2

d)

x = 132

35.

3y = -15

a)

-5

b)

5

c)

-3

d)

3

36.

-4x + 1 = 21

a)

x=120

b)

x=5

c)

x=30

d)

x=-5

37.

-6x = 18

a)

3

b)

-3

c)

6

d)

-6

38.

5 = 7s - 9

a)

2

b)

6

c)

7

d)

8

39.

2b = -16

a)

8

b)

4

c)

-8

d)

3

40.

4a + 3 = 15

a)

2

b)

4

c)

1

d)

3

41.

Which equation has x = 2 as a solution?

a)

3 + x = 10

b)

11 + x = 13

c)

4x = 32

d)

5x =25

42.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

43.

4x + 7 = 23

a)

x = 16

b)

x = 4

c)

x = 9

d)

x = 12

44.

6p - 5 =13

a)

12

b)

15

c)

3

d)

-3

45.

Use the Distributive Property to solve the equation.
4( x + 2) = 16

a)

-2

b)

0

c)

1

d)

2

46.

7x = 3x + 24

a)

6

b)

10

c)

14

d)

4

47.

-8y = -3y -15

a)

3

b)

-3

c)

5

d)

-5

48.

Solve for the variable. 3x=-27

a)

x=9

b)

x=-30

c)

x=-9

d)

x=-24

49.

Translate into an expression:
two more than three times x

a)

3x-2

b)

2>3x

c)

2+3x

d)

2(3x)

50.

Translate into an expression:
4 less than two times a number

a)

4-2x

b)

4<2x

c)

2x-4

d)

2-4

51.

Simplify:
5(3x+1)

a)

15x+1

b)

15x+5

c)

8x+1

d)

8x+6

52.

Solve for d:
-7(6 + d) = 49

a)

13

b)

1

c)

-1

d)

-13

53.

What is the first step in solving this equation:
5x + 7 = 12

a)

Divide by 5

b)

Subtract 5

c)

Multiply by 7

d)

Subtract 7

54.

What is the first step to complete when solving this equation?
10 - 3y = 4

a)

Add 10

b)

Subtract 10

c)

Add 3

d)

Divide by -3

55.

Solve:
2(2t - 3) = 6(t + 2)

a)

t=9

b)

t=4

c)

t=-9

d)

t=-3

56.

3b + 6b = 63

a)

-7

b)

9

c)

7

d)

21

57.

-9(x + 5) + 6 = -12

a)

10

b)

3

c)

4

d)

-3

58.

-7(x - 5)

a)

-7x + 35

b)

-7x - 35

c)

-12x

d)

12x

59.

7a - 2b + 6 + 4b - 5a

a)

12a + 6b + 6

b)

24ab

c)

2a + 2b + 6

60.

-5(x + 3)

a)

-8x

b)

-5x + 3

c)

-5x - 15

d)

-5x - 2

61.

Solve for x: 7 (2x - 4) = 42

a)

x = 2

b)

x = 8

c)

x= 5

d)

x = 9

62.

What operation would you perform first and then second when solving for m in the following equation?

10 + 7m = 17

a)

subtract 10, and then divide by 7

b)

divide by 7, and then subtract 10

c)

multiply by 7, and then subtract 10

d)

add 10, and then multiply by 7

63.

8x + 20 = 2(4x + 10)

a)

x = 8

b)

x = 10

c)

There is no solution.

d)

There are infinite solutions.

64.

88 = 25 + x

a)

x = 113

b)

x = -113

c)

x = -63

d)

x = 63

65.

Solve:
-4x = 24

a)

20

b)

-20

c)

6

d)

-6

66.

Solve:
-8 + 5x - 2 = 20

a)

6

b)

-6

c)

2

d)

-2

67.

Solve:
3(x - 2) = 18

a)

6.7

b)

4

c)

8

d)

-4

68.

Solve:
6(5x - 3) + 2 = 14

a)

2

b)

.5

c)

-1

d)

1

69.

Solve for y:
2y + 7 = 11

a)

y = 2

b)

y = 1

c)

y = 9

d)

y = 4

70.

Solve for b:
3(b - 4) = -3

a)

b = 3

b)

b = -3

c)

b = 5

d)

b = -5

71.

Solve for x:
3x + 2x + 7 = 10x - 16

a)

x = 23/5

b)

x = 9/5

c)

x = 14

d)

x = -8/5

72.

What is the first step to solve this equation:

-3x + 11 = 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.

73.

What is the first step in solving this equation 8x - 6 = 10

a)

Add 6

b)

Subtract 8

c)

Divide by 8

d)

Subtract 6

74.

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

75.

Which property does 5(x+6) = 5x + 30 demonstrate

a)

Associative Property

b)

Distributive Property

c)

Commutative Property

d)

Identity Property of Multiplication

76.

Solve for x:
x + 8 = -3

a)

x = -5

b)

x = 5

c)

x = -11

d)

x = 11

77.

Solve for k:
6k = 30

a)

k = 36

b)

k = 24

c)

k = 180

d)

k = 5

78.

What is the first step in solving this equation 8x - 6 = 10

a)

Add 6

b)

Subtract 8

c)

Divide by 8

d)

Subtract 6

79.

Solve:

-4x = 24

a)

-96

b)

-20

c)

28

d)

-6

80.

Solve:

3(x - 2) = 18

a)

$\frac{20}{3}$

b)

4

c)

8

d)

-4

81.

Determine if the given value is true or false

6x + 5 = 27; x=4

a)

true

b)

false

82.

y + 8 = 20

a)

10

b)

11

c)

12

d)

13

83.

k - 10 = 7

a)

-3

b)

3

c)

17

d)

- 17

84.

- 4T = - 44

a)

- 11

b)

11

c)

- 40

d)

48

85.

What is the first step in the following equation?

2x - 5 = 13

a)

Subtract five from both sides

b)

Divide by two on both sides

c)

Add five to both sides

d)

Multiply by one-fifth on both sides

86.

What is the first step in the following equation?

-5 + 3x = -18

a)

Divide by 3 on both sides

b)

Add eighteen to both sides

c)

Add five to both sides

d)

Subtract five from both sides

87.

What is the first step in the following equation?

28 = -12 - 4x

a)

Subtract twelve from both sides

b)

Add four to both sides

c)

Divide by negative four on both sides

d)

Add twelve to both sides

88.

What is the second step to the following equation?

3x + 12 = 60

a)

Subtract twelve from both sides

b)

Add twelve to both sides

c)

Multiply by three on both sides

d)

Divide by three on both sides

89.

What is the second step to the following equation?

-2 - 4x = -14

a)

Divide by negative four on both sides

b)

Multiply by negative four on both sides

c)

Add two to both sides

d)

Subtract fourteen from both sides

90.

What is the second step to the following equation?

45 = s/6 + 14

a)

Subtract fourteen from both sides

b)

Subtract forty-five from both sides

c)

Divide by six on both sides

d)

Multiply by six on both sides

91.

What is the second step to the following equation?

2/3x + 3 = 15

a)

Add by 3 on both sides

b)

Subtract by 3 on both sides

c)

Multiply by 3/2 on both sides

d)

Divide by 2/3 on both sides

92.

How would you solve the equation?
5x = 30

a)

Subtract 5 from both sides

b)

Subtract 30 from both sides

c)

Multiply both sides by 5

d)

Divide both sides by 5

93.

How would you solve the equation?
36 = 9 + m

a)

Subtract 9 from both sides

b)

Add 9 to both sides

c)

Multiply both sides by 9

d)

Divide both sides by 9

94.

How would you solve the equation?
38 = m - 15

a)

Subtract 15 from both sides

b)

Add 15 to both sides

c)

Multiply both sides by 15

d)

Divide both sides by 15

95.

10 = z + 6

a)

z = 16

b)

z = -16

c)

z = 4

d)

z = -4

96.

q - 12 = 1

a)

q = 13

b)

q = 11

c)

q = -11

d)

q = -13

97.

r / 3 = 7

a)

r = 21

b)

r = 24

c)

r = 10

d)

r = 4

98.

t - 19 = 2

a)

t = 17

b)

t = -17

c)

t = 21

d)

t = -21

99.

24 = 4c

a)

c = 48

b)

c = 20

c)

c = 8

d)

c = 6

100.

8y = 48

a)

y = 8

b)

y = 6

c)

y = 40

d)

y = 56

101.

18 = a/2

a)

a = 9

b)

a = 16

c)

a = 20

d)

a = 36

102.

11 = m - 4

a)

m = 7

b)

m = -7

c)

m = 15

d)

m = 44

103.

1 + s = 3

a)

s = -2

b)

s = 2

c)

s = 3

d)

s = 4

104.

v/5 = 9

a)

v = 45

b)

v = 40

c)

v = 14

d)

v = 4

105.

4x = 44

a)

x = 40

b)

x = 11

c)

x = 48

d)

x = 176

106.

Solve the equation
3x = 27.

a)

x = 24

b)

x = 81

c)

x = 9

d)

x = 3

107.

Which equation has x = 5 as the solution?

a)

x + 15 = 10

b)

2x = 5

c)

2x = 10

108.

What equation matches this situation?
Robyn had some video games then bought 4 more. Now she has a total of 10 games.

a)

v - 4 = 10

b)

v + 4 = 10

c)

10 - 4 = v

d)

Answer not Given

109.

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

a)

Add 62 to each side.

b)

Subtract 62 from each side.

c)

Multiply each side by 62.

d)

Add 123 to each side.

110.

144=12z

a)

z=20

b)

z=11

c)

z=12

111.

What is the inverse operation of multiplication?

a)

Addition

b)

Subtraction

c)

Division

112.

Solve for x. x - 8 = -5

a)

13

b)

-13

c)

3

d)

-3

113.

What is the inverse operation you would use to solve:

6x = 36

a)

Multiply

b)

Divide

c)

Add

d)

Subtract

114.

Solve the equation:

4p = 16

a)

p = 12

b)

p = -12

c)

p = -4

d)

p = 4

115.

t ÷ 6 = 8

a)

48

b)

56

c)

32

d)

14

116.

What does "inverse" mean?

a)

Same as

b)

Opposite

Chapter 6:Solving Equations

Total questions: 116

Worksheet time: 58mins

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