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Linear inequalities

A linear inequality has solutions that are an interval, not a single number. You gather the x-terms on one side and the numbers on the other, just as in an equation. If you divide by a positive number, you keep the inequality sign. A parenthesis means the endpoint is not included, and a bracket that it is. A strict inequality therefore gets a parenthesis.

ax + b < c

linear inequality

x < \frac{c - b}{a}

when a is positive

Symbols

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

Example

$3(x - 2) < 6$ gives $3x - 6 < 6$ , so $3x < 12$ and $x < 4$ .

The boundary is $\dfrac{6 + 6}{3} = 4$ .

Reverse the sign only when you multiply or divide by a negative number.

Practise inequalities and sign charts for free →

← Sign chart · Double inequalities →

Part of Mathematics S1: Inequalities and sign charts.