Solve 3(x + 2) = 21.
- Distribute: 3x + 6 = 21.
- Subtract 6: 3x = 15; divide by 3: x = 5.
- Check: 3(5 + 2) = 21.
Answer: x = 5
Multi-Step Linear Equations Worksheets
Solve linear equations and check the solution by substitution.
Learn the skill
How to solve multi-step equations
To solve an equation, find every value that makes both sides equal. Simplify each side, gather variable terms, and use inverse operations on both sides. Substitution into the original equation checks the result.
A method you can use
- Distribute across parentheses and combine like terms on each side.
- Add or subtract the same expression on both sides to gather variable terms.
- Isolate the variable, then check. A false constant statement means no solution; a true identity means every allowed value works.
Worked examples
Solve 5x − 4 = 2x + 11.
- Subtract 2x: 3x − 4 = 11.
- Add 4 and divide by 3: 3x = 15, so x = 5.
- Both original sides equal 21 at x = 5.
Answer: x = 5
Solve 2(x + 3) = 2x + 9.
- Expand to 2x + 6 = 2x + 9.
- Subtract 2x to get 6 = 9, a false statement.
Answer: No solution
Find the mistake: distributing a negative coefficient
A student turns −2(x − 3) = 10 into −2x − 6 = 10. What should change?
See the reasoning
Multiplying −2 by −3 gives positive 6, so the correct expansion is −2x + 6 = 10.
Subtract 6: −2x = 4. Divide by −2: x = −2.
Check in the original equation: −2(−2 − 3) = −2(−5) = 10. Substitution catches the sign error.
Try a transfer problem
Solve 4 − 3(2x − 1) = 19.
Check the solution
Expand to 4 − 6x + 3 = 19. Combine constants: 7 − 6x = 19, so −6x = 12 and x = −2. The original left side becomes 4 − 3(−5) = 19.
x = −2
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Solve 4x + 7 = 23.
Show answer and explanation
x = 4
Subtract 7 to obtain 4x = 16, then divide by 4.
2. Solve 3x + 2 = x + 12.
Show answer and explanation
x = 5
Subtract x and 2 to get 2x = 10.
Before you begin
Use inverse operations, signed numbers and the distributive property.
Choose your level
- Easy: Solve equations of the form ax + b = c.
- Medium: Distribute a factor before isolating x.
- Hard: Collect variable terms from both sides before solving.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Solve: 4x + 6 = 38
2
Solve: 2x + 6 = 30
3
Solve: 2x + 10 = 18
4
Solve: 8x + 13 = 45
5
Solve: 11x + 5 = 126
6
Solve: 4x + 2 = 10
Answer Key
1. x = 82. x = 123. x = 44. x = 45. x = 116. x = 2