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Solving Equations - Printable Math Worksheets 8th Grade - Wayground

Solving Equations

Mandi Weber

Created by Mandi Weber

22 questions

8th Grade

Math

Updated Oct 2026

Solving Equations is a Grade 8 mathematics worksheet that builds fluency with one-, two-, and multi-step linear equations. Students solve equations with variables on one or both sides, identify inverse operations, apply the rule of maintaining equality, and determine the operation used in a worked step. The worksheet also asks students to translate fixed-fee and per-unit-rate situations into equations, analyze an algebraic error, and select or enter solutions. The 22 questions use multiple-choice, drag-and-drop, dropdown, fill-in-the-blank, and multiple-select formats. Contexts such as gym memberships, car charges, and taxi fares help students connect equations to real-world relationships, while items such as -4x - 14 = 6 require direct symbolic solving. This free printable worksheet includes a complete answer key and is suitable for Grade 8 math practice, review, or assessment.

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Solving Equations

Total questions: 22

Name
Class
Date
1.

r + 11 + 8r = 29r\ +\ 11\ +\ 8r\ =\ 29  

a)

r =0r\ =0  

b)

r = 1r\ =\ 1  

c)

r = 2r\ =\ 2  

d)

r = 3r\ =\ 3  

2.

Solve: 7x = 3x + 24

(a)  

Choose from the below words

10

4

6

14

3.

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

(a)  

Choose from the below words

Find the coefficient

Find the value of the variable

Find the constant

Be confused

4.
Jim paid a gym membership fee of $50, plus $20 per month.  Jim has paid a total of $290 to the gym.  Which equation matches this situation?
a)
50 + 20m = 290
b)
20 + 50m = 290
c)
50 + 20 = m
d)
50m - 20 = 290
5.

−6x + 14 = 26-6x\ +\ 14\ =\ 26  

(a)  

6.

In order to solve an equation, we must get variables on one side of an equation, and constants on the opposite side.

(a)  

Choose from the below words

False

True
7.
Solve for x:
5x - 14 = 8x + 4 (a)  
Choose from the below words
x = 6
x = -6
x = -18/13
x = 10/3
8.
What is the first step to solving this equation?

What is the first step to solving this equation?

a)

add -8 to both sides

b)

subtract -8 to both sides

c)

Multiply -8 to both sides

d)

divide -8 to both sides

9.
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.
10.

Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Scott's car bill was $63.

a)

7x + 35 = 63

b)

7x = 63

c)

7x - 35 = 63

d)

35x + 7 = 63

11.
What is the inverse operation of division? (a)  
Choose from the below words
Division
Multiplication
Addition
Subtraction
12.

What are the two basic rules for solving algebraic equations? (Select 2 answers)

a)

Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

b)

Negative signs can be ignored

c)

Always start on the left side, regardless of where the variable is

d)

Always do the opposite operation

13.

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

14.
What is the error?

What is the error?

a)

Adding 2x to 3x

b)

Subtracting 5 from both sides

c)

Adding 2x to -2x

d)

Dividing by 5 on both sides

15.

Using the math we just saw, solve this equation.

 14 + 3n = 5n − 6\ 14\ +\ 3n\ =\ 5n\ -\ 6  

a)

n = 10

b)

n = -10

c)

n = -18

d)

n = -22

16.

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5. Ann paid a total of $49.10.

What is the equation for this problem?

(a)  

Choose from the below words

$2.10 x = $49.10

$2.10 + $5 = x

$2.10 x + $5 = $49.10

x = $5($2.10)

17.

What is the solution to the equation -4x-14=6?

(a)  

18.
Is the solution below correct?
5d = 2d - 18
-2d   -2d
3d = -18
d = 6
a)
Yes
b)
No
19.

How do you solve this equation?
21=14a21=\frac{1}{4}a  

a)

add both sides by  14\frac{1}{4}  

b)

subtract both sides by  14\frac{1}{4}  

c)

multiply both sides by  14\frac{1}{4}  

d)

divide both sides by  14\frac{1}{4}  

20.

Solve: x + 9 = -3

(a)  

21.

-5k + 10 = -2k - 14

a)

k = 8

b)

k = -8

c)

k = 2

d)

k = -2

22.
What is the inverse operation of subtraction? (a)  
Choose from the below words
Subtraction
Multiplication
Division
Addition
WaygroundAnswer Key

Solving Equations

Total questions: 22

1.
c)

r = 2r\ =\ 2  

2.
6
3.
Find the value of the variable
4.
a) 50 + 20m = 290
5.
-2
6.
True
7.
x = -6
8.
c)

Multiply -8 to both sides

9.
a) Add 62 to each side. 
10.
a)

7x + 35 = 63

11.
Multiplication
12.
a)

Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal sign

, d)

Always do the opposite operation

13.
a)

Subtracted 2x from both sides of the equation

14.
a)

Adding 2x to 3x

15.
a)

n = 10

16.
$2.10 x + $5 = $49.10
17.
-5
18.
b) No
19.
d)

divide both sides by  14\frac{1}{4}  

20.
-12
21.
a)

k = 8

22.
Addition

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FAQs

What does the Solving Equations worksheet cover?

This Grade 8 worksheet focuses on solving one-, two-, and multi-step linear equations, including equations with variables on both sides. Its 22 items use multiple-choice, drag-and-drop, dropdown, fill-in-the-blank, and multiple-select formats to practise inverse operations, preserving equality, identifying solution steps, translating rate-and-fee word problems into equations, and recognizing algebraic errors.

How can I use this worksheet to teach solving linear equations?

Introduce the worksheet by modeling how to isolate a variable using opposite operations and by performing the same operation on both sides of an equation. Then use the step-analysis items to have students explain moves such as subtracting 2x from both sides, followed by the gym, car-charge, and taxi scenarios so they connect coefficients and constants to real-world equations. Finish with the direct-solving and error-analysis questions as independent practice.

What mistakes should I watch for when students complete this equations worksheet?

Watch for students moving a term across the equal sign without applying the corresponding operation to both sides, choosing the wrong inverse operation, or mishandling negative signs in equations such as 5x - 14 = 8x + 4 and -4x - 14 = 6. In the word problems, students may switch the fixed fee and per-unit rate or omit the constant charge, producing an incorrect equation. The step-analysis and error-identification items can reveal whether the issue is procedural or a misunderstanding of equation structure.

How do I assign and grade this Solving Equations worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the 22 responses. For printable submissions, you can scan student work with the Wayground for Teachers app to support grading and review.

How can I differentiate this equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation-solving prompts, answer choices, and word-problem text are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the same practice in solving equations and writing equations from scenarios.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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