GCSE Mathematics Revision — Solving Linear Equations
Revise Solving Linear Equations for GCSE Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Solving Linear Equations?
A linear equation has an unknown raised to the power of 1 (no x² or higher). To solve, isolate the unknown by performing the same operation on both sides. Work through brackets first, collect like terms, then use inverse operations. Equations with the unknown on both sides require you to move all x terms to one side first.
Step-by-step explanationWorked examples
Worked example
Solve 3(2x - 1) = 4x + 7. Expand: 6x - 3 = 4x + 7. Subtract 4x: 2x - 3 = 7. Add 3: 2x = 10. Divide by 2: x = 5.
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Start with low-focus cards for Solving Linear Equations, then move into full exam-style practice when you want the heavier session.
Common mistakes
- 1Not applying an operation to BOTH sides of the equation.
- 2Expanding brackets incorrectly, especially with a negative sign outside: -2(x - 3) = -2x + 6, not -2x - 6.
- 3Dividing only one term by the coefficient instead of the whole side.
- 4Losing track of negative signs when moving terms across the equals sign.
Solving Linear Equations exam questions
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Frequently asked questions
What is the best order of steps for solving equations?
Expand brackets, collect like terms on each side, move unknowns to one side and numbers to the other, then divide by the coefficient of x.
How do I check my answer?
Substitute your answer back into the original equation and verify that both sides are equal.