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Multi Step Solving Equations with Variables on Both Sides - Printable Mathematics Worksheets grade 7 - Wayground

Multi Step Solving Equations with Variables on Both Sides

13 questions

7th - 7th Grade

Mathematics

This Grade 7 mathematics worksheet gives students focused practice solving multi-step linear equations, including equations with variables on both sides. It contains 13 items: 3 fill-in-the-blank problems that require students to enter a numerical solution and 10 multiple-choice questions. The equations include negative coefficients, constants on both sides, and combining like terms, so students must isolate the variable through a logical sequence of inverse operations rather than rely on a single computation. Several questions also assess the solving process directly. Students identify the first step in solving an equation and determine which operation was used between two shown solution steps, reinforcing why the same operation must be applied to both sides. Designed for Grade 7 math practice, review, or formative assessment, this free printable worksheet includes a complete answer key for efficient checking and feedback.

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Worksheets

Multi Step Solving Equations with Variables on Both Sides

Total questions: 13

Name
Class
Date
1.

−6n − 20 = −2n + 4(1 − 3n)

Hint: Enter the number only

(a)  

2.

n + 2 = −14 − n

Hint: Enter the number only

(a)  

3.

 5x - 2 = x + 26    

Hint: Enter the number only

(a)  

4.

Solve

a)

p = -1

b)

p = -3

c)

p = 13/11

d)

p = 1

5.

Solve: -10x + 40 = -80

a)

x = 12

b)

x = 4

c)

x = -12

d)

x = -4

6.
a)

term

b)

coefficient

c)

variable

d)

constant

7.

Solve: 11x - 44 = 9x - 20

a)

x = 12

b)

x = 32

c)

x = -12

d)

x = -32

8.

Solve: 9 - 4x = 12x + 25

a)

x = 2

b)

x = 1

c)

x = -3

d)

x = -1

9.

Solve: 9x + 1 = 64

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 9

10.

Solve: 5x + 15 = 10x - 40

a)

x = 10

b)

x = -10

c)

x = 11

d)

x = -11

11.

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.

12.

Solve the equation for the variable

a)

5

b)

10

c)

12

d)

17

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

Answer Key

Multi Step Solving Equations with Variables on Both Sides

Total questions: 13

1.
3
2.
-8
3.
7
4.
b)

p = -3

5.
a)

x = 12

6.
d)

constant

7.
a)

x = 12

8.
d)

x = -1

9.
b)

x = 7

10.
c)

x = 11

11.
b)

Subtract 11 from both sides

12.
a)

5

13.
a)

Subtracted 2x from both sides of the equation

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FAQs

What does this worksheet cover, and how does it help students solve equations with variables on both sides?

This Grade 7 worksheet practices solving multi-step linear equations, including equations with variables on both sides, negative coefficients, and constants on both sides. Its 3 fill-in-the-blank and 10 multiple-choice items require students to combine like terms, apply inverse operations, identify an appropriate first step, and interpret a worked solution step.

How can I use this worksheet to teach solving multi-step equations with variables on both sides?

Introduce a consistent sequence—simplify each side, move variable terms to one side, move constants to the other, and divide by the coefficient—before assigning the problems. Use the worksheet’s first-step question and the item analyzing Jacob’s solution to have students explain why an operation, such as subtracting 2x from both sides, preserves equality.

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

Watch for students changing a sign incorrectly when moving terms, combining unlike terms, or applying an operation to only one side of an equation. In the fill-in-the-blank items, check that students enter the solution number rather than an expression; in the process questions, look for confusion between subtracting a term from both sides and performing the next inverse operation.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses from the digital quiz on Wayground.

How can I differentiate this worksheet for my students?

For the equations, answer choices, and fill-in-the-blank prompts on this worksheet, use Advanced Settings to adjust font spacing and font size for easier reading. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the mathematical directions and expressions.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across 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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