Solving Linear Equations

A linear equation is an equation where the highest power of the unknown is 1. Solving a linear equation means finding the value of the unknown that makes the equation true. This is one of the most frequently tested skills in the AQA GCSE Mathematics exam and appears on both Foundation and Higher tier papers.

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The Golden Rule

Whatever you do to one side of an equation, you must do the same to the other side. Think of the equals sign as a balance — both sides must remain equal at all times.

flowchart LR
    A[Equation] --> B[Identify what is being done to the unknown]
    B --> C[Undo operations in reverse order]
    C --> D[Simplify each step]
    D --> E[Isolate the unknown on one side]
    E --> F[Check by substituting back]

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One-Step Equations

These require just one operation to isolate the unknown.

Worked Example 1

Solve: x + 7 = 12

Subtract 7 from both sides: x = 12 - 7 x = 5

Worked Example 2

Solve: 3x = 18

Divide both sides by 3: x = 18 / 3 x = 6

Worked Example 3