Solving linear equations step by step (with examples)
Learn the balance method for solving linear equations, including brackets and x on both sides, with worked examples for GCSE and Algebra 1.
KS3GCSEMiddle SchoolHigh SchoolCurriculum fit: GCSE Maths Algebra (Foundation and Higher). US: Grade 8 and Algebra I linear equations (Reasoning with Equations and Inequalities).
On this page
What is it?
A linear equation has an unknown value, usually written as x, that is not squared or raised to any other power. Solving the equation means finding the value of x that makes it true.
The method is the balance idea: whatever you do to one side of the equation, you must do to the other. You use inverse operations to get x on its own.
Key formulas and ideas
- Inverse operations: add and subtract undo each other; multiply and divide undo each other.
- Do the same to both sides to keep the equation balanced.
- When x appears on both sides, collect the x terms on one side first.
- Check by substituting your answer back into the original equation.
Worked examples
Example 1: Two steps
Question: Solve 3x + 5 = 20.
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check: 3 × 5 + 5 = 20.
Answer: x = 5
Example 2: With brackets
Question: Solve 2(x + 3) = 14.
- Expand: 2x + 6 = 14.
- Subtract 6: 2x = 8.
- Divide by 2: x = 4.
Answer: x = 4
Example 3: x on both sides
Question: Solve 5x − 3 = 2x + 9.
- Subtract 2x from both sides: 3x − 3 = 9.
- Add 3: 3x = 12.
- Divide by 3: x = 4.
Answer: x = 4
Common mistakes
- Doing an operation to one side only.
- Making sign errors when moving a term, such as turning −3 into −3 instead of +3.
- Forgetting to multiply every term inside a bracket.
- Not checking the answer.
Practice questions
Frequently asked questions
How do I check my answer?
Substitute your value back into the original equation. If both sides are equal, it is correct.
What if I get a fraction as an answer?
That is fine. Many equations have fractional or negative solutions, so leave the answer as a simplified fraction or decimal.
Related guides
Simplifying algebraic expressions: collecting like terms
Collect like terms, multiply and divide algebraic terms and simplify expressions with brackets, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolRearranging formulae: how to change the subject
Make any letter the subject of a formula using inverse operations, with worked examples including squares and square roots.
GCSEHigh SchoolSolving inequalities and showing them on a number line
Solve linear inequalities, including double inequalities, and remember to reverse the sign when dividing by a negative, with worked examples.
GCSEHigh SchoolSources and review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.