1Cademy - Addition Property of Inequality

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Linear Inequality

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Addition Property of Inequality

The Addition Property of Inequality states that adding the same quantity to both sides of an inequality does not change the direction of the inequality. For any numbers $a$ , $b$ , and $c$ :

If $a < b$ , then $a + c < b + c$

If $a > b$ , then $a + c > b + c$

The same rule holds for $\leq$ and $\geq$ . This property is used to solve inequalities in which a number has been subtracted from the variable. To isolate the variable, the same number is added to both sides — just as with equations — and the inequality symbol stays pointed in the same direction. For example, to solve $x - 5 < 8$ , adding $5$ to both sides gives $x < 13$ , and the $<$ symbol remains unchanged.

Updated 2026-05-03

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University of Michigan - Ann Arbor

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