GCSE & IGCSE maths practice

Solving linear equations questions and answers

To solve a linear equation, do the same thing to both sides until the letter is on its own. Undo the operations in reverse order: get rid of added or subtracted numbers first, then divide. With brackets, expand them first; with the unknown on both sides, collect the letters on one side; with fractions, multiply everything by the denominator.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Linear equations: lesson and examples

Where solving linear equations comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: solve linear equations in one unknown algebraically, including those with the unknown on both sides and with brackets.
Cambridge IGCSE (0580)	Core and Extended: solve linear equations in one unknown. Extended: fractional equations with numerical and linear algebraic denominators.

The method

Expand any brackets.
Collect the letter terms on one side and the numbers on the other.
Divide by the number in front of the letter.
Fractions: multiply every term by the denominator (or the LCM of the denominators) first.
Check by substituting your answer back in.

Solving linear equations questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Solve $3x + 5 = 17$

x =

Question 2Warm-upFoundation

Solve $\dfrac{x}{4} - 2 = 3$

x =

Exam-style

Question 3Exam-styleFoundation

Solve $5x - 3 = 2x + 12$

x =

Question 4Exam-styleFoundation

Solve $4(x + 3) = 2x + 20$

x =

Question 5Exam-styleFoundation

Solve $7 - 2x = 3(x + 4)$

x =

Question 6Exam-styleFoundation

Solve $\dfrac{2x + 1}{3} = x - 2$

x =

Challenge

Question 7ChallengeFoundation

A rectangle has sides $(x + 3)$ cm and $(2x - 1)$ cm. Its perimeter is 34 cm. Find $x$ .

x =

Question 8ChallengeFoundation

Solve $\dfrac{x + 1}{2} - \dfrac{x - 2}{5} = 3$

x =

Common mistakes

Doing different things to the two sides.
Expanding a bracket and multiplying only the first term.
Losing a minus sign when moving terms across.
Multiplying only some of the terms by the denominator.

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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