All courses › Mathematics S1 › Inequality and a negative factor

Inequality and a negative factor

An inequality is solved almost like an equation, with one important exception. If you multiply or divide by a negative number, you reverse the inequality sign. If you multiply by a positive number, the sign stays. A minus sign in front of x is the same as multiplying by negative one, so the sign must be reversed. Check the answer by inserting one number from the solution set and one number outside it.

Symbols

Example

$-2x > 6$. Divide by $-2$ and reverse the sign: $x < -3$, because $\dfrac{6}{-2} = -3$.

$x = -4$ works, $x = 0$ does not.

← Equations with fractions · A linear cost model →

Part of Mathematics S1: Algebra and equations.