Chapter 6.2, Problem 35STP

To determine

To solve: the given inequality and then to graph the solution set..

Explanation of Solution

Given information:

The inequality $\left|\frac{2p-8}{4}\right|\ge 9$

Calculation:

Consider $\left|\frac{2p-8}{4}\right|\ge 9$

  $\begin{array}{l}-9\ge \frac{2p-8}{4}\ge 9\\ -36\ge 2p-8\ge 36\\ -28\ge 2p\ge 44\\ -14\ge p\ge 22\\ p\ge 22\text{ or }p\le -14\end{array}$

Hence, the solution set is $(-\infty ,-14]\cup [22,\infty )$

Graph:

The graph of solution set of the inequality $\left|\frac{2p-8}{4}\right|\ge 9$ is shown below.

  

Hence, the shaded region is the solution of the given inequality.