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Linear Equations in One Variable — A Clear Walkthrough

Mathematics Class 8 Linear EquationsEnglishStandard

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What a linear equation is, the golden rule for solving one, and three fully worked examples including equations with variables on both sides.

What is a linear equation?

An equation where the highest power of the variable is 1, for example 2x + 3 = 11. Solving it means finding the value of x that makes both sides equal.

The golden rule

Whatever you do to one side, do to the other. Your goal is to get x alone on one side.

Worked examples

2x + 3 = 11 → subtract 3: 2x = 8 → divide by 2: x = 4.
5x − 7 = 3x + 5 → bring x terms together: 5x − 3x = 5 + 7 → 2x = 12 → x = 6.
(x/3) + 4 = 9 → subtract 4: x/3 = 5 → multiply by 3: x = 15.

Always check

Put your answer back into the original equation. For example 2(4) + 3 = 11 ✓. If both sides match, you're correct.

Exam tip: In word problems, name the unknown as x first, write one sentence as one equation, then solve.

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