What is the Division Property of Inequality? Definition and Examples
What is the division property of inequality? The division property of inequality is the process of dividing each side of an inequality by the same number in order to find an equivalent inequality and also see how it affects the inequality.
Dividing an inequality by a positive number
For every real number a, b, and c (c ≠ 0 and c > 0)
If a > b, then a / c > b / c
If a < b, then a / c < b / c
12 > 6, so 12 / 3 > 6 / 3 (or 4 > 2)
6 < 12, so 6 / 3 < 12 / 3 (or 2 < 4)
Dividing an inequality by a negative number
For every real number a, b, and c (c ≠ 0 and c < 0)
If a > b, then a / c < b / c
If a < b, then a / c > b / c
12 > 6, so 12 / -3 < 6 / -3 (or -4 < -2)
6 < 12, so 6 / -3 < 12 / -3 (or -2 > -4)
The main thing to notice is that when dividing an inequality by a negative number, you need to reverse the inequality sign.
Furthermore, the division property of inequality also applies when the inequality sign is ≤ or ≥.
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