2(3x + 4) − 5 = 4x + 9
Show answer
x = 3
Free printable worksheet
Solving Multi-Step Equations Worksheet
Fourteen full-width equations requiring distribution, combining like terms, and variables on both sides.
Algebra 1Grades 7-104 pagesAnswer key included
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What this worksheet includes
- Fourteen full-width equations requiring distribution, combining like terms, and variables on both sides.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this solving multi-step equations worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach solving multi-step equations
Multi-step equations combine several algebra skills in one problem. The most reliable order is to simplify each side first, move variable terms to one side, move constants to the other, and divide only after the variable term is isolated.
The worksheet deliberately includes equations that require distribution, combining like terms, and collecting variables from both sides. Its full-width layout leaves enough space to keep each transformation readable.
Learning objectives
- Simplify both sides before isolating the variable
- Choose efficient operations when variables appear on both sides
- Recognize identities and contradictions when they occur
Skills to review first
- Linear-equation basics
- Signed-number arithmetic
- Distributing and combining like terms
Worked example
Follow the reasoning step by step
Solve 4(2x − 3) − 5 = 3(x + 4) − 4.
- Distribute on both sides: 8x − 12 − 5 = 3x + 12 − 4.
- Combine like terms: 8x − 17 = 3x + 8.
- Subtract 3x and add 17: 5x = 25.
- Divide by 5: x = 5.
Solution: x = 5; substituting gives 23 on both sides.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
5x − 2(3x − 7) = 19
Show answer
x = −5
4(y + 1) + 2y = 3(y − 2) + 19
Show answer
y = 3
Error check
Common mistakes to watch for
- Trying to isolate x before simplifying each side
- Combining terms that are not like terms
- Dividing one term instead of every term in an equation