1Cademy - Solving $$-8q < 32$$ and $$\frac{k}{-12} \leq 15$$

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Division Property of Inequality

Example

Solving $-8q < 32$ and $\frac{k}{-12} \leq 15$

Solve each inequality by applying the appropriate property of inequality, reversing the inequality sign when multiplying or dividing by a negative number.

ⓐ Solve $-8q < 32$ : Divide both sides by $-8$ . Since $-8$ is negative, the inequality reverses: $q > -4$ In interval notation, the solution is $(-4, \infty)$ .

ⓑ Solve $\frac{k}{-12} \leq 15$ : Multiply both sides by $-12$ . Since $-12$ is negative, the inequality reverses: $k \geq -180$ In interval notation, the solution is $[-180, \infty)$ .