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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Next step: Changing the Subject
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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.
Mini lesson for Solving Linear Equations
1. Understand the core idea
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.
Can you explain Solving Linear Equations without copying the notes?
2. Turn it into marks
Solve 3(2x - 1) = 4x + 7. Expand: 6x - 3 = 4x + 7.
Underline the method, evidence, or command-word move that would earn credit in GCSE Algebra.
3. Fix the likely mark leak
Watch for this mistake: Not applying an operation to BOTH sides of the equation.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Solving Linear Equations. Free to start; sign in to save progress.
Solving Linear Equations practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Solving Linear Equations is testing.
Answer: 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.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Solving Linear Equations question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Not applying an operation to BOTH sides of the equation." What should their next repair task be?
Answer: Do one Solving Linear Equations question and review the mistake type.
Mark focus: Error correction and next-step practice.
Solving Linear Equations flashcards
Core idea
What is the main idea in 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.
Common mistake
What mistake should you avoid in Solving Linear Equations?
Not applying an operation to BOTH sides of the equation.
Practice
What is one useful practice task for Solving Linear Equations?
Answer one Solving Linear Equations question and review the mistake type.
Exam board
How should you use board notes for Solving Linear Equations?
Use your own GCSE specification for exact paper wording and depth.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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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.