Knowledge Organiser: Linear Equations
This topic summary covers Knowledge Organiser: Linear Equations within Linear Equations for GCSE Mathematics. Revise Linear Equations in Algebra for GCSE Mathematics with 16 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
16 questions
Recall
12 flashcards
Knowledge Organiser: Linear Equations
Key Terms
- Equation: A mathematical statement that two expressions are equal
- Linear equation: An equation where the highest power of x is 1 (e.g. 3x + 7 = 22)
- Solution: The value of x that makes the equation true
- Inverse operation: The opposite operation (+ and − are inverses; × and ÷ are inverses)
- Balance method: Whatever you do to one side, do the same to the other
Must-Know Facts
- Solve by doing inverse operations in reverse order of BIDMAS
- Deal with + and − before × and ÷
- When x appears on both sides: collect all x terms on one side first
- Equations with fractions: multiply both sides by the denominator first
- Always check your answer by substituting back into the original equation
- Expand brackets before solving if they appear
Key Methods
- ax + b = c: subtract b from both sides, then divide both sides by a
- ax + b = cx + d: collect x terms → (a−c)x = d−b → divide
- Fractions: multiply every term by the LCM of denominators
- Brackets: expand first, then solve
Common Mistakes
- Not applying operations to both sides: Whatever you do to one side, you must do to the other — adding 5 to the left means adding 5 to the right too
- Moving terms without changing sign: When moving a term across the equals sign it changes sign — 3x + 7 = 22 → 3x = 22 − 7
- Not expanding brackets first: Expand before collecting — 2(x + 3) = 10 becomes 2x + 6 = 10, not 2x + 3 = 10
- Not checking the answer: Always substitute your solution back into the original equation to verify both sides balance
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Read this section alongside the surrounding pages in Linear Equations. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Linear Equations
What is the solution to 3x = 12?
Solve x + 7 = 15
Quick Recall Flashcards
16 questions on Linear Equations — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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