Solving Linear Equations — GCSE Mathematics Revision
Revise Solving Linear Equations for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Solving Linear Equations in GCSE Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising GCSE Mathematics for UK exams.
- Exam boards
- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, Cambridge International (CIE), SQA, IB, AP).
- Free plan
- Sign up free to use tutor paths and full feedback on your answers. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
Topic has curated content entry with explanation, mistakes, and worked example. [auto-gate:promote; score=72.25]
Next in this topic area
Next step: Changing the Subject
Continue in the same course — structured practice and explanations on StudyVector.
Go to Changing the SubjectWhat 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 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.
Practise this topic
Jump into adaptive, exam-style questions for Solving Linear Equations. Free to start; sign in to save progress.
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
Exam-style questions for Solving Linear Equations with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
Solving Linear Equations exam questionsGet help with Solving Linear Equations
Get a personalised explanation for Solving Linear Equations from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorFree full access to Solving Linear Equations
Sign up in 30 seconds to unlock step-by-step explanations, exam-style practice, instant feedback and on-demand coaching — completely free, no card required.
Try a practice question
Unlock Solving Linear Equations practice questions
Get instant feedback, step-by-step help and exam-style practice — free, no card needed.
Start Free — No Card NeededAlready have an account? Log in
Step-by-step method
Step-by-step explanation
4 steps · Worked method for Solving Linear Equations
Core concept
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 ter…
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.