How to solve linear equations, step by step

A linear equation has the variable to the first power only, with no $x^2$ or higher. Solving it means undoing whatever is done to $x$, one operation at a time, until $x$ stands alone. Whatever you do to one side you must do to the other.

Start with the basic moves

Undo addition and subtraction first, then multiplication and division. Take $3x + 5 = 20$.

Variables on both sides

When $x$ appears on both sides, gather the variable terms on one side and the numbers on the other. Take $5x - 3 = 2x + 9$.

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Clearing fractions and parentheses

Fractions and brackets are easier once you remove them. Expand parentheses, and multiply through by a common denominator to clear fractions. Take $\tfrac{x}{2} + 1 = \tfrac{x}{3} + 3$.

Always check your answer

Put your value back into the original equation. For $x = 12$ above, the left side is $\tfrac{12}{2} + 1 = 7$ and the right side is $\tfrac{12}{3} + 3 = 7$. They match, so the answer holds.

The pattern never changes: simplify each side, move the variable to one side, then isolate it.