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Solving Multi-Step Equations with Variables on Both Sides Worksheet PDF

Solving multi-step equations is an important algebra skill for students in 7th and 8th grade. These equations require several steps, such as using the distributive property, combining like terms, and using inverse operations to isolate the variable.

This Solving Multi-Step Equations Worksheet PDF gives students printable practice with a variety of equations designed for middle school math. Students can work through each problem step by step and check their solutions using the answer key.

The worksheet includes equations with integers, parentheses, combining like terms, and variables on both sides. It is useful for classroom practice, homework, math centers, review, and extra practice at home.

Download and print the free worksheet PDF to help students build accuracy and confidence when solving multi-step equations.

Multi-Step Equations Step-by-Step Quiz

Solving Multi-Step Equations

Problem 1 of 3

Quiz Complete! 🎉

Great job practicing your step-by-step equation solving.

Free Solving Multi-Step Equations Worksheet PDF:

Practice solving multi-step equations with integers, parentheses, combining like terms, and variables on both sides.

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Solving Multi-Step Equations Worksheet PDF
Download Worksheet with Answers
Solving Multi-Step Equations Worksheet PDF With Answer Key

Printable PDF: Download, print, and solve the problems by hand.

Answer Key: Check your work after completing the worksheet.

What Are Multi-Step Equations?

A multi-step equation is an equation that requires more than one operation to solve for the variable.

For example:

3x + 5 = 20

First subtract 5 from both sides:

3x + 5 - 5 = 20 - 5

3x = 15

Then divide both sides by 3:

3x = 15

\(\frac{3x}{3}\) = \(\frac{15}{3}\)

x = 5


Solving multi-step equations worksheet for Grades 7–8 students

How to Solve Multi-Step Equations

Step 1: Simplify both sides

Use the distributive property and combine like terms when necessary.


Step 2: Move variable terms to one side

Use addition or subtraction to get the variable terms on one side of the equation.


Step 3: Move constants to the other side

Use inverse operations to isolate the variable term.


Step 4: Divide or multiply

Use the inverse operation to get the variable by itself.


Step 5: Check your answer

Substitute the value of the variable back into the original equation.


Example of Solving a Multi-Step Equation:

Solve: 3(x + 4) - 5 = 22

Solution:

     3(x + 4) - 5 = 22

Distribute 3: Multiply the terms inside the parentheses.

     3x + 12 - 5 = 22

Combine like terms: Subtract 5 from 12

     3x + 7 = 22

Subtract 7 from both sides: 

     3x + 7 - 7 = 22 - 7 

     3x = 15

Divide by 3:

     \(\frac{3x}{3}\) = \(\frac{15}{3}\)

     x = 5

Check

Substitute 5 into the original equation:

     3(5 + 4) - 5 = 22

     27 - 5 = 22

     22 = 22 ✓

Therefore:

     x = 5


How to Solve Equations with Variables on Both Sides:

Step-by-Step Example:

Solve for x: 3(x - 4) = 2x + 7

Solution:

3(x - 4) = 2x + 7

Step I: Distribute. Multiply the terms inside the parentheses.

            3x - 12 = 2x + 7

Step II: Move variables to one side. Subtract 2x from both sides.

            3x - 12 - 2x = 2x + 7 - 2x

            x - 12 = 7

Step III: Isolate the variable. Add 12 to both sides.

            x - 12 + 12 = 7 + 12

           x = 19


Solving Multi-Step Equations Worksheet

Part A — Basic Multi-Step Equations

1. 3x + 7 = 25

2. 5x - 9 = 31

3. 4x + 6 = 30

4. 7x - 8 = 34

5. 6x + 11 = 47

Show Answers
1. x = 6

2. x = 8

3. x = 6

4. x = 6

5. x = 6



Part B — Distribution

6. 2(x + 5) = 24

7. 3(x - 4) = 18

8. 4(x + 2) - 3 = 25

9. 5(x - 2) + 4 = 29

10. 2(x + 7) - 6 = 20

Show Answers
6. x = 7

7. x = 10

8. x = 5

9. x = 7

10. x = 6



Part C — Combining Like Terms

11. 3x + 5 + 2x = 30

12. 7x - 4 - 2x = 21

13. 4x + 8 + 3x = 36

14. 9x - 5 - 4x = 20

15. 6x + 3 + 2x = 35

Show Answers
11. x = 5

12. x = 5

13. x = 4

14. x = 5

15. x = 4



Part D — Variables on Both Sides

16. 5x + 8 = 2x + 23

17. 7x - 4 = 3x + 20

18. 9x + 2 = 5x + 30

19. 6x - 7 = 2x + 17

20. 8x + 5 = 3x + 30

Show Answers
16. x = 5

17. x = 6

18. x = 7

19. x = 6

20. x = 5



Common Mistakes When Solving Multi-Step Equations:

1. Forgetting to distribute to every term

Incorrect:

3(x + 4) = 3x + 4

Correct:

3(x + 4) = 3x + 12

2. Changing only one side

Whatever operation is performed on one side of an equation must also be performed on the other side.

3. Combining unlike terms

Students should remember that terms such as 4x and 7 cannot be combined.

4. Making sign errors

Pay special attention when subtracting negative numbers or distributing a negative number.

5. Not checking the solution

Substituting the answer back into the original equation helps catch calculation mistakes.

Free Download Multi-Step Equations Worksheet — Grade 7–8

  • Solving Multi-Step Equations with Integers Worksheet with Answer Key
  • Multi-Step Equations with Fractions Worksheet with Answer Key
  • Multi-Step Equations with Variables on Both Sides with Answer Key

This worksheet is designed for students working on middle school algebra skills in 7th and 8th grade. It can be used for:

  • Classroom Practice
  • Independent Practice
  • Homework
  • Math Intervention
  • Test Preparation
  • Review before an Algebra Assessment
  • Tutoring
  • Homeschool Math Practice


Play Multi-Step Equations Quiz Online:

Solving Multi-Step Equations Quiz | Grades 7–8

Solving Multi-Step Equations Quiz

Grades 7–8 • Solve each equation one step at a time. Choose the best next step, then complete the equation.

Question 1 of 10 0%
Score 0
Streak 0
Question 1

Solve the equation step by step:

3x + 7 = 25

Step 1: What should you do next?

3x + 7 = 25

Worked Solution

    Tip: Whatever operation you perform on one side of an equation, perform the same operation on the other side.

    Quiz Complete!

    0/10

    Answer Review

    # Equation Your Result Correct Answer

    Frequently Asked Questions about Solving Multi-Step Equations with Variables on Both Sides Worksheet:

    What is a multi-step equation?

    Answer:

    A multi-step equation is an equation that requires several operations to find the value of the variable.

    How do you solve a multi-step equation?

    Answer:

    Simplify both sides, combine like terms, move variable terms and constants using inverse operations, isolate the variable, and check the solution.

    What grade teaches multi-step equations?

    Answer:

    Multi-step equations are commonly taught as part of middle school algebra, particularly in 7th and 8th grade, depending on the curriculum.

    Can I print this multi-step equations worksheet?

    Answer:

    Yes. The worksheet should be available as a printable PDF that students can download and complete by hand.

    Does the worksheet include an answer key?

    Answer:

    Yes. Include a separate answer key or an answer-key section so students, parents, and teachers can check the completed work.

    What skills are practiced?

    Answer:

    Students can practice the distributive property, combining like terms, inverse operations, integer arithmetic, and solving equations with variables on one or both sides.

    What does it mean when an equation has variables on both sides?

    Answer:

    An equation has variables on both sides when a variable term appears on the left and right sides of the equation. Students use addition or subtraction to move the variable terms to one side before isolating the variable.

    How do you solve an equation with variables on both sides?

    Answer:

    First simplify each side, then use addition or subtraction to move the variable terms to one side. Next isolate the variable using inverse operations and check the solution in the original equation.

    About Author

    Priyanka Ghosh, Founder of Math Only Math

    Written by Priyanka Ghosh
    Mathematics Educator | Founder of Math Only Math

    Priyanka Ghosh has been teaching elementary and middle-school mathematics for over 12 years and specializes in creating simple, child-friendly math lessons and worksheets.

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