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Linear equations in one unknown

2026-10-13Equations & Inequalities Mr Yip

Solve linear equations with brackets and fractions using balanced steps and clear checking.

Key formulas

If a = b then a + c = b + c

If a = b \text{then ka} = kb

ax + b = c \rightarrow x = (c - b)/a

Balance principle

Whatever you do to one side, do to the other. Prefer inverse operations: undo addition with subtraction, undo multiplication with division.

Brackets and fractions

Expand brackets first, or clear fractions by multiplying through by the LCM of denominators. Collect unknown terms on one side and constants on the other.

Checking

Substitute your solution back into the original equation. A check takes seconds and catches arithmetic errors before marks are lost.

Exam habit

Number each transformation. Never cancel terms that are added rather than multiplied.

Worked example

Clear fractions

Problem. Solve (2x)/5 − 1 = 3.

Solution. Add 1: (2x)/5 = 4. Multiply by 5: 2x = 20. x = 10. Check: 20/5 − 1 = 3.

Review quiz

1 / 4

Solve 3x − 7 = 11

Practice questions

Solve 3x − 7 = 11.
Solve 2(x + 4) = 3x − 1.
Solve (x/3) + 5 = 9.

Study notes

What if the variable disappears?

If you get a true statement (e.g. 0 = 0), every number works; if false (e.g. 0 = 5), there is no solution. Linear S2–S3 questions usually have one solution.

Should I use a calculator?

Keep exact fractions unless the paper asks for decimals.