Solve 7x − 3 = 4x + 12.
- Subtract 4x: 3x − 3 = 12.
- Add 3 and divide by 3.
Answer: x = 5
Variables on Both Sides Worksheets
Solve linear equations by applying the same operation to both sides and check by substitution.
Learn the skill
Equations with variables on both sides
When both sides contain a variable, collect its terms on one side using the same operation on both sides. Simplification may give one solution, no solution, or an identity true for every value.
A method you can use
- Expand parentheses and combine like terms within each side.
- Subtract a variable term from both sides, then isolate the remaining variable.
- Check in the original equation; if the variable disappears, decide whether the remaining statement is true or false.
Worked examples
Solve 2(x + 4) = 2x + 8.
- Expand to 2x + 8 = 2x + 8.
- Subtracting both matching expressions gives 0 = 0.
Answer: All real numbers
Solve 3x + 1 = 3x − 2.
- Subtract 3x to obtain 1 = −2.
- No input can make this false statement true.
Answer: No solution
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Solve 5x + 1 = 2x + 10.
Show answer and explanation
x = 3
Subtract 2x and 1 to get 3x = 9.
2. Solve 4x + 6 = 4x + 2.
Show answer and explanation
No solution
Subtract 4x to get the false statement 6 = 2.
Before you begin
Use signed arithmetic, substitute values and read expressions with variables.
Choose your level
- Easy: Use positive integers and one-step relationships.
- Medium: Use signed values or two steps.
- Hard: Combine operations or reverse a relationship.
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: 3x + 5 = 2x + 13.
2
Solve: 2x + 5 = 1x + 17.
3
Solve: 2x + 8 = 1x + 12.
4
Solve: 6x + 11 = 5x + 15.
5
Solve: 8x + 4 = 4x + 48.
6
Solve: 3x + 2 = 1x + 6.
Answer Key
1. x = 82. x = 123. x = 44. x = 45. x = 116. x = 2