AAAarubi AcademyGCSE Maths Edexcel first
Join nowSign in
GCSE Maths / Edexcel

Solving linear equations

Solve one-step, two-step, bracketed, and both-sides linear equations while keeping working balanced.

AlgebraFoundation and HigherGrades 3 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Solving linear equations

Pearson Edexcel GCSE Maths algebra A17: solve linear equations in one unknown, including equations with the unknown on both sides.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Solving an equation means finding the value of the unknown that makes the left side and right side equal.

Think of an equation like a balance. Whatever you do to one side, you must do to the other side.

Use inverse operations to undo the equation. Addition is undone by subtraction, multiplication is undone by division, and brackets are usually expanded first.

For a two-step equation, remove the added or subtracted number first, then divide or multiply to find the unknown.

If the unknown appears on both sides, collect the unknown terms on one side and number terms on the other before dividing.

A good final check is to substitute your answer back into the original equation.

Key ruleKeep the equation balanced: whatever you do to one side, do to the other side.

Worked examples

Two-step equation

Solve 3x - 4 = 14.

  1. Undo the -4 first by adding 4 to both sides: 3x = 18.
  2. 3x means 3 multiplied by x, so divide both sides by 3.
  3. x = 6.

Answer: x = 6

Unknown on both sides

Solve 5x + 2 = 2x + 17.

  1. Subtract 2x from both sides: 3x + 2 = 17
  2. Subtract 2: 3x = 15
  3. Divide by 3: x = 5

Answer: x = 5

Bracketed equation

Solve 4(x - 2) = 20.

  1. Expand the bracket: 4x - 8 = 20
  2. Add 8: 4x = 28
  3. Divide by 4: x = 7

Answer: x = 7

Common mistakes

  • Changing one side of the equation but not the other.
  • Moving terms across the equals sign without changing the operation correctly.
  • Dividing before collecting all the x terms.
  • Forgetting to expand brackets before solving.

Quick exercise

Try these before moving to the exam-style questions.

  1. Solve x + 8 = 15.
  2. Solve 4x = 28.
  3. Solve 2x - 5 = 13.
  4. Solve 3x + 4 = x + 18.
  5. Solve 5(x - 2) = 20.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Solve 3x + 5 = 20.

linear equationsinverse operationsfoundation algebra
Standard exam styleFoundation and HigherNon-calculator3 marks

Solve 4x - 7 = 2x + 9.

unknown on both sidesbalancing equationsmethod marks
ChallengeHigherEither4 marks

A rectangle has length 3x + 2 and width x + 5. Its perimeter is 46 cm. Find x.

forming equationsperimetersolving equationshigher reasoning