Free Printable Math 8 - Unit 2 Review Solving Equations and Inequalities

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.

What would be the last step in solving the following equation, if you divide both sides by -2 first?

$-2\left(3x\ +\ 4\right)=-32$

a)

Subtracting 4 from both sides.

b)

Multiplying both sides by 3.

c)

Adding 4 to both sides

d)

Dividing both sides by 3.

32.

What is the answer?

3x + 2 = -5x + 10

a)

x = 1

b)

x = -1

c)

x = 6

d)

x = -6

33.

If I wanted to start to simplify this equation what would I do in order to get variables on one side and constants on the other?

2x - 6 = 3x

a)

Move the 2x to the other side of the equation by adding it to both sides.

b)

Move the 6 to the other side of the equation by adding it to both side.

c)

Move the 2x to the other side of the equation by subtracting it from both sides.

d)

Move the 6 to the other side of the equation by subtracting it from both sides.

34.

What property did I use from step 1 to step 2?

Step 1: 2(x + 3) + 7 = 10x - 11

Step 2: 2x + 6 + 7 = 10x - 11

a)

Distributive Property

b)

Combine like terms

c)

Addition Property of Equality

d)

Subtraction Property of Equality

35.

Reorder the following based on which properties I used in solving the following equation;

$\frac{2}{3}\left(6x\ -9\right)+2\ =\ 7x\ -5$

Step 1: 4x - 6 + 2 = 7x - 5

Step 2: 4x - 4 = 7x - 5

Step 3: -4 = 3x - 5

Step 4: 1 = 3x

Step 5: $\frac{1}{3}=x$

a)

Distributive Property

b)

Combine Like Terms

c)

Subtraction Property of Equality

d)

Addition Property of equality

e)

Division Property of Equality

1)

2)

3)

4)

5)

36.

Use the distributive property to simplify the following, fill in the blank with the correct number. Be sure to look closely at what was already written out for you.

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

-6x + _=-9x

(a)

37.

Solve for x.

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

a)

x = 1

b)

x = 5

c)

x = -1

d)

x = -5

38.

How do you feel about solving equations with variables on both sides? What is difficult? What do you find easy?

4 lines

39.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

40.

Solve the inequality and graph its solution:
-2x + 5 < x - 7. Which value is in the solution set?

a)

2

b)

4

c)

-1

d)

5

41.

Solve the inequality and graph its solution:
-4a < 2(a + 5). Which value is NOT in the solution set?

a)

-5

b)

0

c)

1

d)

3

42.

Solve the inequality and graph its solution:
-6v > -4(v + 1). Which value is in the solution set?

a)

1

b)

2

c)

0

d)

10

43.

55c + 13 ≤ 75c + 39

a)

c≤10/13

b)

c ≥ −10/13

c)

-c>19

d)

c≤50/80

44.

30b + 53 ≥ 18b − 83

a)

b≥−34/3

b)

b≥-14 2/3

c)

b>8

d)

-b<12

45.

54x + 64 ≥ 49x + 59

a)

x≥−1

b)

x≤-1

c)

x>9

d)

x<-3

46.

Solve:
3(x - 2) < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

47.

Solve:
6x + 3 > 4x - 7

a)

x>5

b)

x>-5

c)

x<-5

d)

x>-2

48.

Solve:
4(2a + 3) < 3(a - 1)

a)

a<-3

b)

a>-3

c)

a<3

d)

a>3

49.

Solve:
7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

50.

Solve:
14x + 12 < 9x -3

a)

x < -3

b)

x < 5

c)

x < -5

d)

x > 3

51.

Solve:
11x + 16 < 43 + 2x

a)

x < 5

b)

x < 3

c)

x > 5

d)

x > 3

52.

6(L+3) < 3(2L+6)

a)

L > 0

b)

L < 0

c)

All real numbers

d)

No solution

53.

8g − 5g − 4 ≤ -3 + 3g

a)

g ≤ 0

b)

g ≤ 1

c)

All Real Numbers

d)

No Solution

54.

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x ≤ -2

55.

a)

m < 6

b)

m < -6

c)

m > 6

d)

m > -6

56.

a)

a ≥ 4

b)

a ≥ -4

c)

a ≤ 4

d)

a ≤ -4

57.

a)

x < 1

b)

x < -1

c)

x > 1

d)

x > -1

58.

a)

x > 1

b)

x > -1

c)

x < 1

d)

x < -1

59.

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x ≤ -2

60.

Solve:
4(2a + 3) < 3(a - 1)

a)

a<-3

b)

a>-3

c)

a<3

d)

a>3

61.

8g − 5g − 4 ≤ -3 + 3g

a)

g ≤ 0

b)

g ≤ 1

c)

All Real Numbers

d)

No Solution

62.

Solve:
11x + 16 < 43 + 2x

a)

x < 5

b)

x < 3

c)

x > 5

d)

x > 3

63.

Solve:
14x + 12 < 9x -3

a)

x < -3

b)

x < 5

c)

x < -5

d)

x > 3

64.

Solve:
7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

65.

Solve:
3(x - 2) < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

66.

a)

x ≤ 4

b)

x ≤ -4

c)

x ≥ 4

d)

x ≥ -4

67.

a)

n ≤ 6

b)

n ≤ -6

c)

n ≥ 6

d)

n ≥ -6

68.

a)

a ≥ 4

b)

a ≥ -4

c)

a ≤ 4

d)

a ≤ -4

69.

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x ≤ -2

70.

a)

x > 1

b)

x > -1

c)

x < 1

d)

x < -1

71.

a)

x < 1

b)

x < -1

c)

x > 1

d)

x > -1

72.

a)

a ≥ 4

b)

a ≥ -4

c)

a ≤ 4

d)

a ≤ -4

73.

8g − 5g − 4 ≤ -3 + 3g

a)

g ≤ 0

b)

g ≤ 1

c)

All Real Numbers

d)

No Solution

74.

6(L+3) < 3(2L+6)

a)

L > 0

b)

L < 0

c)

All real numbers

d)

No solution

75.

Find the solution to the inequality: $6x+2<10+4x$

a)

$x<4$

b)

$x<8$

c)

$x>4$

d)

$x>8$

76.

-2(x - 5) = 12 - 3x

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 5

d)

x = 2

77.

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

a)

No Solution

b)

Infinitely Many Solutions

c)

x = .63

d)

x = 1.6

78.

x + 6 = x

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 0

d)

x = 6

79.

3x - 1 = 1 - 3x

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 1/3

d)

x = 3

80.

4x - 9 = 3.5x - 9

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 0

d)

x = 0.5

81.

3x + 15 = 3(x + 5)

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 0

d)

x = 3

82.

5.5 - x = -4.5 - x

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 5

d)

x = -0.5

83.

2x + 4 = - (-7x + 6)

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 2

d)

x = 5

84.

6(7x + 7) = 7(6x + 6)

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 1/2

d)

x = 1

85.

1/2x + 1/2x = x + 1

a)

No Solution

b)

Infinitely Many Solutions

c)

x = 1/2

d)

x = 1

86.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

87.

How many solutions does the equation have
6x + 3 = 6x + 3

a)

One Solution

b)

No Solution

c)

Infinite Solutions

88.

x = x

a)

No Solution

b)

One Solution

c)

Infinite Solutions

d)

Beyond Solutions

89.

Identify the number of solutions for the equation below:

$3x-5=2x+4$

a)

No Solution

b)

One Solution

c)

Infinite Solutions

90.

Identify the number of solutions for the equation below:

-2x+7=-2x+7

a)

No Solution

b)

One Solution

c)

Infinite Solutions

91.

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

92.

Match the following correctly.

a)

$-5=-5$

1.

Infinite Solutions

b)

$0=3$

2.

No Solution

c)

$x=12$

3.

One Solution

93.

Consider the unfinished equation: $12\left(x-3\right)+18=$ ________. Match the following expression with the number of solutions the equation would have with that expression on the right hand side.

a)

$6\left(2x-3\right)$

1.

Infinite Solutions

b)

$4\left(3x-3\right)$

2.

No Solution

c)

$4\left(2x-3\right)$

3.

One Solution

94.

Match the following correctly

a)

One Solution

1.

Different variable terms on each side.

b)

No Solution

2.

Same variable term, diff constants

c)

Infinite Solutions

3.

Same variable and constants on each side

95.

Select all that apply:

One solution: 4x + 2 =

a)

= 4x - 3

b)

= 9x + 1

c)

= x + 2

d)

= 3(2x - 7)

e)

= 2x + 2x + 2

96.

Select all that apply:

No solution: 3(x + 6) =

a)

= 3x + 18

b)

= x + 5

c)

= 3x + 12

d)

= 3x + 1

e)

$3x-18$

97.

Select all that apply:

Infinite solutions: 4x + 8 + 2x =

a)

= 6x + 2

b)

= 6x + 8

c)

= 2(3x + 4)

d)

= 2x + 8

e)

= 8 + 6x

98.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

99.

Solve:
3x + 15 = 3(x + 5)

a)

No Solution

b)

x = 15

c)

Infinitely Many Solutions

100.

What is the solution to the equations?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

101.

Does the following equation have one solution, no solutions, or infinitely many solutions?

2x + 4 = 2x + 4

a)

One

b)

None

c)

Infinite

d)

This cannot be determined

102.

Does the following equation have one solution, no solutions, or infinitely many solutions?

5x + 4 = 2x + 4

a)

One

b)

None

c)

Infinite

d)

This cannot be determined

103.

Identify the property used to simplify.

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Distributive Property

d)

Multiplication Property of Equality

e)

Division Property of Equality

104.

Identify the property used to simplify.

a)

Subtraction Property of Equality

b)

Addition Property of Equality

c)

Distributive Property

d)

Associative Property (Combining Like Terms)

e)

Division Property of Equality

105.

Determine the type of solution you will have if you get
-6=6

a)

one solution

b)

infinite solution=identity

c)

no solution

d)

I don't know. I need to study.

106.

Determine the type of solution you will have if you get
x=0.25

a)

one solution

b)

infinite solution=identity

c)

no solution

d)

I don't know. I need to study.

107.

Determine the type of solution you will have if you get
2+3=6

a)

one solution

b)

infinite solution=identity

c)

no solution

d)

I don't know. I need to study.

108.

$5x+4=5x+4$

a)

one solution

b)

no solution

c)

infinite solutions

109.

$3\left(x+4\right)=3\left(x-8\right)$

a)

one solution

b)

no solution

c)

infinite solutions

110.

$6x=5x$

a)

one solution

b)

no solution

c)

infinite solutions

111.

$4-2x=2x-4$

a)

one solution

b)

no solution

c)

infinite solutions

112.

$x+9\ =\ x-9$

a)

one solution

b)

no solution

c)

infinite solutions

113.

$-2\left(x+1\right)=x-3x-2$

a)

one solution

b)

no solution

c)

infinite solutions

114.

How many solutions does the equation have
-2 ( -4x + 7 ) = -2 + 4x

a)

One Solution

b)

No Solution

c)

Infinite Solutions

115.

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

a)

No Solution

b)

One Solution

c)

Infinite Solution

116.

How many solutions does the equation have
4 ( 8n - 1 ) = 19 + 32n

a)

One Solution

b)

No Solution

c)

Infinite Solutions

Math 8 - Unit 2 Review Solving Equations and Inequalities

Total questions: 116

Worksheet time: 10hrs 2mins

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