x + 9 = 17
Show answer
x = 8
Free printable worksheet
Solving Linear Equations Worksheet
Thirty carefully spaced problems covering one-step, two-step, multi-step, and contextual linear equations, with a complete answer key.
Algebra 1Grades 7-105 pagesAnswer key included
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What this worksheet includes
- Thirty carefully spaced problems covering one-step, two-step, multi-step, and contextual linear equations, with a complete answer key.
- 5-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 linear 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 linear equations
A linear equation is balanced when both sides represent the same value. Solving it means using inverse operations to isolate the variable while performing the same operation on both sides.
This practice moves from one-step equations into distribution, variables on both sides, and equations written in context. Students should record each transformation on a new line and substitute the solution into the original equation to verify it.
Learning objectives
- Use inverse operations while preserving equality
- Solve equations with distribution and variables on both sides
- Check a solution by substitution
Skills to review first
- Integer operations
- Combining like terms
- The distributive property
Worked example
Follow the reasoning step by step
Solve 4(x − 3) + 7 = 2x + 9.
- Distribute: 4x − 12 + 7 = 2x + 9.
- Combine like terms: 4x − 5 = 2x + 9.
- Subtract 2x, then add 5: 2x = 14.
- Divide by 2: x = 7.
Solution: x = 7; both sides equal 25 when x is 7.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
3x − 5 = 16
Show answer
x = 7
5(x − 2) = 3x + 8
Show answer
x = 9
Error check
Common mistakes to watch for
- Changing only one side of the equation
- Missing a negative sign while distributing
- Checking the final line instead of the original equation