EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Algebra · Foundation & Higher

Solving linear equations

A linear equation contains an unknown (usually x) to the power 1. You solve it by doing the same operation to both sides until x is isolated.

Revising solving linear equations the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Solving linear equations GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Whatever you do to one side, you must do to the other.
  • 2Aim to get all x terms on one side and all numbers on the other.
  • 3If there are brackets, expand them first.
  • 4If there are fractions, multiply every term by the denominator to clear them.
  • 5Check your answer by substituting back into the original equation.
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Worked examples

Example 1

Solve 3x + 7 = 22

Working

  1. Subtract 7 from both sides: 3x = 15
  2. Divide both sides by 3: x = 5
  3. Check: 3(5) + 7 = 22 ✓
Answerx = 5
Example 2

Solve 5(2x − 3) = 4x + 9

Working

  1. Expand the bracket: 10x − 15 = 4x + 9
  2. Subtract 4x from both sides: 6x − 15 = 9
  3. Add 15 to both sides: 6x = 24
  4. Divide by 6: x = 4
Answerx = 4
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Common mistakes

✗Forgetting to expand brackets fully before rearranging.
✗Making sign errors when moving terms across the equals sign.
✗Dividing by the coefficient of x before moving all x terms to one side.
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Exam tips

✓Always check your answer — it takes 10 seconds and earns no marks but prevents costly mistakes.
✓If x appears on both sides, collect x terms first.

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