Chapter 5.2, Problem 2AGP

To determine

To find the value of $n$ that satisfied the inequality $-\frac{n}{6}\le 8$ and show on the number line.

Answer to Problem 2AGP

The value of $n$ that satisfied the inequality $-\frac{n}{6}\le 8$ is $n\ge -48$ and the number line is given as:

  

Explanation of Solution

Given:

The inequality is given as $-\frac{n}{6}\le 8$ .

Concept Used:

• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Properties of inequality:

  1. $b\le c\Rightarrow ab\le ac,\text{ if }a\ge 0$

  2. $b\le c\Rightarrow ab\ge ac,\text{ if }a\le 0$

Calculation:

Simplify the inequality $-\frac{n}{6}\le 8$ for the value of $n$ .

Multiply both sides by 6:

  $\begin{array}{c}-\frac{n}{6}\le 8\\ 6\cdot -\frac{n}{6}\le 6\cdot 8\\ -n\le 48\end{array}$

Multiply both side by -1 to change the inequality:

  $\begin{array}{c}-n\le 48\\ \left(-n\right)\left(-1\right)\ge 48\left(-1\right)\\ n\ge -48\end{array}$

The value of $n$ in the number line is:

  

Hence, the value of $n$ that satisfied the inequality $-\frac{n}{6}\le 8$ is $n\ge -48$ .