Wayground
Modeling Equations with Variables on Both Sides - Printable Mathematics Worksheets grade 7 - Wayground

Modeling Equations with Variables on Both Sides

15 questions

7th - 8th Grade

Mathematics

Modeling Equations with Variables on Both Sides is a free printable mathematics worksheet for students in Grades 7–8. It contains 15 multiple-choice items in which students examine visual models and select the equation that accurately represents each model. The equations include variables and constants on both sides, positive and negative terms, and varying coefficients, such as equations written with x or n. This worksheet strengthens students’ ability to translate a model into an algebraic equation before attempting to solve it. Students must attend to the location, sign, and coefficient of each term, making the activity useful for checking equation-writing accuracy and identifying misunderstandings about two-sided expressions. A complete answer key is included for efficient review, reteaching, or independent practice.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Modeling Equations with Variables on Both Sides

Total questions: 15

Name
Class
Date
1.

Write the equation for the model.

a)

2x - 2 = -x - 8

b)

-x - 2x = 2x - 8x

c)

-x - 2 = 2x - 8

2.

Write the equation for the model.

a)

3x + 1 = -x + 5

b)

-x + 1 = 3x + 5

c)

-x + x = 3x + 5x

3.

Write the equation for the model.

a)

-x + 2 = 2x - 1

b)

-x + 2x = 2x - x

c)

2x + 2 = -x - 1

4.

Write the equation for the model.

a)

3x + x = -x - 3x

b)

-x + 1 = 3x - 3

c)

3x + 1 = -x - 3

5.

Write the equation for the model.

a)

-2x - 1 = 2x - 9

b)

2x - 1 = -2x - 9

c)

-2x - 9 = 2x - 1

6.

Write the equation for the model.

a)

-x - 4 = 3x

b)

3x + 4 = -x

c)

3x - 4 = -x

7.

Write the equation for the model.

a)

2x - 4 = x - 7

b)

2x + 4 = x + 7

c)

x - 4 = 2x - 7

8.

Write the equation for the model.

a)

2x + 7 = -3x + 2

b)

2x - 2 = 3x - 7

c)

2x + 2 = -3x + 7

9.

Write the equation for the model.

a)

2x + 3 = x + 1

b)

2x + 1 = x + 3

c)

2x - 1 = x - 3

10.
a)

-x - 4 = 2x + 2

b)

-x - 2 = 2x - 4

c)

-x + 2 = 2x - 4

11.

Write the equation for the model.

a)

5x + 5 = 3x + 1

b)

5x - 1 = 3x + 5

c)

5x + 1 = 3x + 5

12.

Write the equation for the model.

a)

3x - 7x = 2x + 5x

b)

3x + 5 = 2x - 7

c)

3x - 7 = 2x + 5

13.

Write the equation for the model.

a)

2x - 2 = -x + 7

b)

2x + 2 = x + 7

c)

2x + 7 = -x - 2

14.

Write the equation for the model.

a)

3x + 8 = x

b)

3x = x + 8x

c)

3x = x + 8

15.

Write the equation for the model.

a)

3n - 6 = -n + 4

b)

3n + 4 = -n - 6

c)

3n + 4n = -n - 6n

Answer Key

Modeling Equations with Variables on Both Sides

Total questions: 15

1.
c)

-x - 2 = 2x - 8

2.
b)

-x + 1 = 3x + 5

3.
a)

-x + 2 = 2x - 1

4.
c)

3x + 1 = -x - 3

5.
a)

-2x - 1 = 2x - 9

6.
c)

3x - 4 = -x

7.
a)

2x - 4 = x - 7

8.
c)

2x + 2 = -3x + 7

9.
b)

2x + 1 = x + 3

10.
c)

-x + 2 = 2x - 4

11.
c)

5x + 1 = 3x + 5

12.
c)

3x - 7 = 2x + 5

13.
a)

2x - 2 = -x + 7

14.
c)

3x = x + 8

15.
b)

3n + 4 = -n - 6

Browse by subjects

Browse by grades

Browse by format

FAQs

What does the Modeling Equations with Variables on Both Sides worksheet cover?

This Grade 7–8 mathematics worksheet asks students to use visual models to select the equation that represents each situation. Across 15 multiple-choice items, students identify variable terms and constants on both sides, including positive and negative coefficients, before solving is attempted.

How can I use this worksheet to teach writing equations from models?

First, model how to read each side of a visual model and translate its terms in the same order, including the sign and coefficient. Then have students justify why one option matches the model while the distractors reverse sides, change signs, or attach constants to the wrong terms. Use the 15 multiple-choice items for guided practice before assigning the worksheet independently.

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

Students may reverse the left and right sides, overlook a negative sign, or confuse a coefficient with a constant when selecting an equation. The distractors also target errors such as changing subtraction to addition or placing a number with the wrong variable term, so ask students to match every term in the model to its equation before choosing an answer.

How do I assign and grade this worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital version supports online completion and grading.

How can I differentiate this equations-from-models worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font so the multiple-choice equations are easier to compare term by term. You can also apply a dyslexia-friendly font or translate the equation prompts and answer choices into another language while keeping the model-based task intact.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive 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.

© 2026 Wayground Inc.

Accessibility and Inclusion