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Writing & Solving Equations with Variables on Both Sides - Printable Mathematics Worksheets class 7 - Wayground

Writing & Solving Equations with Variables on Both Sides

12 questions

7th - 7th Grade

Mathematics

This Grade 7 mathematics worksheet gives students 12 multiple-choice questions on writing and solving linear equations with variables on both sides. Students translate real-world situations into equations that compare two changing quantities, such as follower totals, savings balances, putt-putt costs, bus fares, rental charges, and video rentals. They then determine when the quantities become equal, using values such as days, weeks, games, rides, or miles. The worksheet also includes algebraic equations that require students to solve for the variable, including equations with negative coefficients. As a free printable worksheet with an answer key, it supports guided practice, independent work, review, or a quick check of Grade 7 equation-solving skills. The paired “write an equation” and “solve the equation” items help teachers see whether students can both model a situation and find the value that makes two expressions equal.

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Worksheets

Writing & Solving Equations with Variables on Both Sides

Total questions: 12

Name
Class
Date
1.

WRITE AN EQUATION TO REPRESENT THE SITUATION


Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day.

a)

400 - 75x = 1,000 + 25x

b)

400 + 75x = 1,000 – 25x

c)

400x - 75 = 1,000x + 25

d)

400x + 75 = 1,000x – 25

2.

SOLVE THE EQUATION


Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day. How many days will it take them to have the same number of followers?

a)

4 days

b)

5 days

c)

6 days

d)

7 days

3.

WRITE AN EQUATION TO REPRESENT THE SITUATION


Peter and his friends are going to play putt-putt. At one location, they can pay $2.00 for rentals plus $7.50 per game. At another location, it would cost $8.00 for rentals plus $6.00 per game.

a)

2 + 7.50x = 8 + 6x

b)

2 - 7.50x = 8 - 6x

c)

2x + 7.50 = 8x + 6

d)

2x - 7.50x = 8 x- 6

4.

SOLVE THE EQUATION


Peter and his friends are going to play putt-putt. At one location, they can pay $2.00 for rentals plus $7.50 per game. At another location, it would cost $8.00 for rentals plus $6.00 per game. How many games would they have to play in order for either location to cost the same amount?

a)

2 games

b)

3 games

c)

4 games

d)

5 games

5.

WRITE AN EQUATION TO REPRESENT THE SITUATION


Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week.

a)

155x - 10 = 230x + 15

b)

155x + 10 = 230x – 15

c)

155 - 10x = 230 + 15x

d)

155 + 10x = 230 – 15x

6.

SOLVE THE EQUATION


Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week. After how many weeks will their savings accounts have the same amount of money in them?

a)

8 weeks

b)

7 weeks

c)

4 weeks

d)

3 weeks

7.

WRITE AN EQUATION TO REPRESENT THE SITUATION


Kimberly takes the bus to work. The bus ride to work costs her $2.50 each time. She could buy a bus pass for a one-time fee of $15.00 and would then only pay $1.00 each time to ride the bus.

a)

2.50 + x = 15x

b)

2.50x = 15x + 1

c)

2.50x = 15 + x

d)

2.50x = 15x

8.

SOLVE THE EQUATION


Kimberly takes the bus to work. The bus ride to work costs her $2.50 each time. She could buy a bus pass for a one-time fee of $15.00 and would then only pay $1.00 each time to ride the bus. How many times would she have to take the bus in order for the cost to be the same?

a)

5 times

b)

10 times

c)

12 times

d)

15 times

9.
7x = 4x + 33
a)
3
b)
11
c)
21
d)
88
10.
-7x - 36 = 20 -3x
a)
-12
b)
-14
c)
15
d)
8
11.
A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 
a)
30 + 0.15x = 36 + 0.10x
b)
30 - 0.15x = 36 - 0.10x
c)
30 + 36 = 0.10x + 0.36x
d)
36 - 30 = 0.36x + 0.10x
12.
I can join video club A for $25.00 and rent videos for $1.00 each. Or, I can join video club B for $15.00 and rent videos for $2.00 each. Write an equation that could be used to determine how many rentals would be needed for the price to be equal.
a)
25 - x = 15 - 2x
b)
25 + 15 = x + 2x
c)
25x + 1 = 15x + 2
d)
25 + x = 15 + 2x
Answer Key

Writing & Solving Equations with Variables on Both Sides

Total questions: 12

1.
b)

400 + 75x = 1,000 – 25x

2.
c)

6 days

3.
a)

2 + 7.50x = 8 + 6x

4.
c)

4 games

5.
d)

155 + 10x = 230 – 15x

6.
d)

3 weeks

7.
c)

2.50x = 15 + x

8.
b)

10 times

9.
b) 11
10.
b) -14
11.
a) 30 + 0.15x = 36 + 0.10x
12.
d) 25 + x = 15 + 2x

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FAQs

What does the “Writing & Solving Equations with Variables on Both Sides” worksheet cover?

This Grade 7 worksheet uses 12 multiple-choice questions to practice modeling and solving equations with variables on both sides. Students write equations from comparison situations—such as two savings plans or rental costs—and solve for when the amounts are equal, then solve algebraic equations such as 7x = 4x + 33 and -7x - 36 = 20 - 3x.

How can I use this worksheet to teach writing and solving equations with variables on both sides?

First, have students identify each situation’s starting amount, rate, and variable before choosing an equation that represents both expressions. Use the paired modeling-and-solving questions—for example, the follower and putt-putt scenarios—to ask students why each quantity is added or subtracted and what the solution represents. Finish with the symbolic equations so students connect the real-world model to algebraic solution steps.

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

Students may switch a starting amount with a rate, place a one-time fee beside the variable, or use the wrong sign for a quantity that is decreasing, such as followers or savings. In the cost comparisons, check that students match each fixed fee and per-use charge to the correct expression. When solving the symbolic items, students may combine terms incorrectly across both sides or lose a negative sign while isolating the variable.

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 for all 12 multiple-choice questions. For printed responses, you can grade student work by scanning it with the **Wayground for Teachers** app. The printable format also gives schools an option for reducing screen time during equation practice.

How do the equation-writing and equation-solving questions work together on this worksheet?

The worksheet first asks students to choose an equation that represents situations involving two changing quantities, such as 2 + 7.50x = 8 + 6x for two putt-putt locations. Follow-up questions ask students to solve those equations and interpret the answer as the number of days, games, weeks, or rides needed for equal amounts. This sequence checks both mathematical modeling and solving, rather than testing either skill in isolation.

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. Teachers can browse more resources at https://wayground.com/en-us/worksheets.

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