Chapter 6.3, Problem 32PPS

To determine

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

Explanation of Solution

Given information:

The inequality $|2k+7|>7$

Calculation:

Consider $|2k+7|>7$

  $\begin{array}{l}|2k+7|>7\\ -7>2k+7>7\\ -7-7>2k>7-7\\ -14>2k>0\\ -7>k>0\\ k>0\text{ or }k<-7\end{array}$

Hence, the solution set is $(-\infty ,-7)\cup (0,\infty )$

Graph:

The graph of solution set of the inequality $|2k+7|>7$ is shown below.

  

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