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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.
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Free Solving Multi-Step Equations Worksheet PDF:
Practice solving multi-step equations with integers, parentheses, combining like terms, and variables on both sides.
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
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
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
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
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
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:
Question 1
Solve the equation step by step:
3x + 7 = 25
Step 1: What should you do next?
3x + 7 = 25
Tip: Whatever operation you perform on one side of an equation, perform the same operation on the other side.
Quiz Complete!
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Answer Review
| # | Equation | Your Result | Correct Answer |
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Frequently Asked Questions about Solving Multi-Step Equations with Variables on Both Sides Worksheet:
Answer:
A multi-step equation is an equation that requires several operations to find the value of the variable.
Answer:
Simplify both sides, combine like terms, move variable terms and constants using inverse operations, isolate the variable, and check the solution.
Answer:
Multi-step equations are commonly taught as part of middle school algebra, particularly in 7th and 8th grade, depending on the curriculum.
Answer:
Yes. The worksheet should be available as a printable PDF that students can download and complete by hand.
Answer:
Yes. Include a separate answer key or an answer-key section so students, parents, and teachers can check the completed work.
Answer:
Students can practice the distributive property, combining like terms, inverse operations, integer arithmetic, and solving equations with variables on one or 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.
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
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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