Free Printable Solving Equations and Inequalities Practice

1.

12x = 144

a)

x = 12

b)

x = 4

c)

x = 2

d)

x = 132

2.

3y = -15

a)

-5

b)

5

c)

-3

d)

3

3.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

4.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

5.

8x ≥ -32

a)

x ≥ -4

b)

x ≥ 4

c)

x ≤ -4

d)

x ≥ 4

6.

-2(x+2) < 14

a)

x < - 5

b)

x > -5

c)

x < -9

d)

x > -9

7.

2x + 5 = -17

a)

x = -6

b)

x = -12

c)

x = 11

d)

x = -11

8.

-3x - 10 = 2

a)

x = 8/3

b)

x = - 8/3

c)

x = -4

d)

x = 4

9.

22.95 = 16.15 + 4x

a)

x = 9.775

b)

x = 4.2

c)

x = 1.7

d)

x = 2.2

10.

Which of the following represents the solution to the inequality shown below?

-6x - 8 > -32

a)

x < 4

b)

x > 4

c)

x < $6\frac{2}{3}$

d)

x > $6\frac{2}{3}$

11.

Which of the following represents the solution to the inequality shown below?

$-2x\ -\ 3<\ 9$

a)

x < -3

b)

x < -6

c)

x > -3

d)

x > -6

12.

$\frac{X}{8}$ + 10 = 11

a)

x = -8

b)

x = 8

13.

Solve the inequality.

$2\left(b\ -\ 8\right)\ >\ 12$

a)

b > 20

b)

b > 6

c)

b > 14

d)

b > 20

14.

What inequality does the number line graph represent?

a)

x ≤ -4

b)

x ≥ -4

c)

x < -4

d)

x < 4

15.

Which graph matches the inequality
k < 3?

a)

A

b)

B

c)

C

d)

D

16.

-2(x + 3) - 5 = 11

a)

x = - 11

b)

x = 2

c)

x = 11

d)

x = -2

17.

4x + 2(x - 6) = 12

a)

x = 6

b)

x = 4

c)

x = 2

d)

x = -2

18.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

19.

Solve:
$\frac{1}{2}\left(2x+6\right)=3x+13$

a)

No Solution

b)

x = 8

c)

x = -5

d)

x = 7

20.

Find the error in the problem below

19 - 2k = 3k - 1

+3k +3k

19 + 1k = -1

-19 -19

k = -20

a)

They should have divided by 1 for the last step

b)

They should add 19 instead of subtracting 19

c)

I can not find an error

d)

Instead of adding 3k they should subtract 3k

21.

Which of the following equations would have infinite solutions?

a)

3x + 9 = 2x + 9

b)

8x = 8x + 4

c)

3(4x + 4) = 12x +4

d)

-5x + 10 = 10 - 5x

22.

Solve the inequality

a)

b)

c)

d)

23.

The given equation has

a)

no solution

b)

infinitely many solution

c)

one solution

d)

none of the above

24.

How many solutions does the following equation have:

2(9x – 6) = 6(3x – 2) + 2

a)

One solution

b)

Two solutions

c)

No solution

d)

Infinitely many: all real numbers

25.

Distribute and simplify

a)

15x + 135

b)

15x + 9

c)

39x + 9

d)

39x + 135

26.

Solve the following inequality:
-4x + 14 ≤ 54

a)

x ≥ -10

b)

x ≤ -10

c)

x ≥ 17

d)

x ≤ 17

27.

Solve for x

3x − 8 ≥ 4(x − 1.5)

a)

x ≥ 3.5

b)

x ≤ 3.5

c)

x ≥ −2

d)

x ≤ −2

28.

.

When graphing an inequality, you use a closed circle when you use which symbols?

a)

≤, ≥

b)

<, >

29.

The variable, k, is being divided by 11. How should you isolate the variable?

a)

Divide both sides by 11

b)

Add 11 to both sides.

c)

Multiply both sides by 11.

d)

Subtract 11 to both sides.

30.

What is the inverse operation of division?

a)

Division

b)

Addition

c)

Multiplication

d)

Subtraction

31.

.

Solve the inequality.

a)

x ≥ 8

b)

x ≤ 8

c)

x ≥ 18

d)

x ≤ 18

32.

Solve the Equation

2x + 6 = 12

a)

1,000

b)

1

c)

3

d)

12

33.

Solve the Equation:

4 + $\frac{k}{2}$ = -3

a)

2

b)

15

c)

-14

d)

14

34.

$\frac{x}{-2}+3=-3$

a)

$x=0$

b)

$x=12$

c)

$x=-3$

d)

$x=-6$

35.

x + 4 = -3

a)

-1

b)

4

c)

-7

d)

8

36.

-10k = 50
k =

a)

-500

b)

-5

c)

-7

d)

3

37.

The inverse operation of addition is _______________.

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

38.

What is the inverse operation of multiplication?

a)

Addition

b)

Subtraction

c)

Division

d)

Multipication

39.

What do you do to solve this problem?

-6x = 30

a)

Add 6 to both sides

b)

Subtract 6 from each side

c)

Multiply -6 by both sides

d)

Divide -6 by both sides

40.

What is the inverse of division?

a)

Addition

b)

Division

c)

Multiplication

d)

Subtraction

41.

What is the inverse of addition?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

42.

Solve for x. (Use the image to identify the correct inequality and graph.)

$x\ -\ 1\ \le\ -9$

a)

A

b)

B

c)

C

d)

D

43.

Solve for c. (Use the image to identify the correct inequality and graph.)

$c\ -\ 5\ \le\ 6$

a)

A

b)

B

c)

C

d)

D

44.

Solve for x. (Use the image to identify the correct inequality and graph.)

$\frac{x}{8}\ >\ 4$

a)

A

b)

B

c)

C

d)

D

45.

Solve the inequality.

$-5x\ -\ 7\ <\ 28$

a)

x > -7

b)

x < -7

c)

x > $\frac{21}{5}$

d)

x < $\frac{-21}{5}$

46.

Solve and graph the inequality.
7n - 1 > 76

a)

A

b)

B

c)

C

d)

D

47.

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

48.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

49.

When you graph an inequality, you use a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

50.

What would be the best first step to solving the equation?
-3=x+5

a)

add 3 to both sides

b)

subtract 5 from both sides

c)

add 5 to both sides

d)

subtract -5 from both sides

51.

Solve for x:
8x - 10 = -34

a)

4

b)

3

c)

-3

d)

-24

52.

Solve 9 + 3x = 10

a)

2/3

b)

1/3

c)

-1/3

d)

4

53.

4x = 72

a)

x = 18

b)

x = 68

c)

x = 288

d)

x = 62

54.

z - 33 = 234

a)

z = 267

b)

z = 231

c)

z = 317

d)

z = 281

55.

6x = 6

a)

36

b)

1

c)

12

d)

0

56.

-12 = -4x

a)

x = 3

b)

x = -3

c)

x = 4

d)

x = -4

57.

19 + a = -50

a)

a = -950

b)

a = -69

c)

a = -31

d)

a = -50/19

58.

x - 8 = -5

a)

13

b)

-13

c)

3

d)

-3

59.

5. 6b = 30

a)

x = 36

b)

x = 24

c)

x = 180

d)

x = 5

60.

7. -4y = 48

a)

x = -52

b)

x = -12

c)

x = -44

d)

x = -13

61.

Solve the equation below:

a)

k = 152

b)

k = 176

c)

k = 5

d)

k = 27

62.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

63.

8+3h = 26

a)

6

b)

7

c)

8

d)

9

64.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

65.

^r∕₅ -15 = 18

a)

115

b)

15

c)

165

d)

35

66.

7k - 5 = 9

a)

14

b)

10

c)

3

d)

2

67.

6x + 25 = 73

a)

x = 8

b)

x = -8

c)

x = 9

d)

x = -9

68.

Do I need to flip my sign?
3x ≥ 12

a)

Yes

b)

No

69.

Do I need to flip my sign? -3x ≥ 12

a)

Yes

b)

No

70.

Solve for x:

a)

x = 20

b)

x = 7

c)

x = 10

d)

x = 3

71.

a)

y<139

b)

y≥55

c)

y>55

d)

y≤139

72.

-3x ≤ 18

a)

x ≤ -6

b)

x ≤ 6

c)

x ≥ 6

d)

x ≥ -6

73.

19 + a = -50

a)

a = -950

b)

a = -69

c)

a = -31

d)

a = -50/19

74.

x - 8 = -5

a)

13

b)

-13

c)

3

d)

-3

75.

5. 6b = 30

a)

x = 36

b)

x = 24

c)

x = 180

d)

x = 5

76.

7. -4y = 48

a)

x = -52

b)

x = -12

c)

x = -44

d)

x = -13

77.

Solve the equation below:

a)

k = 152

b)

k = 176

c)

k = 5

d)

k = 27

78.

144=12z

a)

z=20

b)

z=11

c)

z=12

79.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

80.

a)

x ≤ -2

b)

x < -2

c)

x ≥ -2

d)

x > -2

81.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

82.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

83.

8+3h = 26

a)

6

b)

7

c)

8

d)

9

84.

^r∕₅ -15 = 18

a)

115

b)

15

c)

165

d)

35

85.

⅙x+7 = 15

a)

1.3333

b)

132

c)

48

d)

15

86.

7k - 5 = 9

a)

14

b)

10

c)

3

d)

2

87.

9f - 9 = 18

a)

f = 3

b)

f = -3

c)

f = 8

d)

f = -8

88.

6x + 25 = 73

a)

x = 8

b)

x = -8

c)

x = 9

d)

x = -9

Solving Equations and Inequalities Practice

Total questions: 88

Worksheet time: 4hrs 51mins

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