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Linear inequalities

A linear inequality is solved in the same way as an equation, but the answer is an interval and not a single number. You can add and subtract on both sides without changing the inequality sign. If you multiply or divide by a negative number, the sign must be flipped, because the number line is mirrored. A positive number keeps the sign.

ax + b > c

linear inequality

\text{divide by a negative} \Rightarrow \text{flip the sign}

the only new rule

Symbols

$a$	the coefficient of x
$x$	the unknown

Example

$-2x > 6$ . Divide by $-2$ and flip the sign: $6/(-2) = -3$ , so $x < -3$ .

Check the answer with one number inside the interval and one outside.

Practise inequalities and sign charts for free →

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Part of Mathematics 1T: Inequalities and sign charts.