1Cademy - Solving $$\frac{n}{-2} \geq 8$$

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Multiplication Property of Inequality

Example

Solving $\frac{n}{-2} \geq 8$

Solve the linear inequality $\frac{n}{-2} \geq 8$ by applying the Multiplication Property of Inequality.

Step 1 — Multiply both sides by $-2$ : Because the variable $n$ is divided by a negative number, multiplying both sides by $-2$ requires reversing the inequality sign:
$-2 \cdot \frac{n}{-2} \leq -2 \cdot 8$

Step 2 — Simplify: Evaluate the product on the right side:
$n \leq -16$

Step 3 — Write the solution in interval notation: The solution includes $-16$ and all real numbers less than $-16$ , which is written as $(-\infty, -16]$ .