Chapter 6.1, Problem 67SR

To determine

To solve: the inequality and plot the solution set for $\left|r+2\right|>6$ .

Answer to Problem 67SR

The solution set is $n\in \left(-\infty ,-8\right)\text{or}\left(4,\infty \right)$ .

Explanation of Solution

Given:

The inequality is $\left|r+2\right|>6$ .

Calculation:

Solve the inequality as follows:

  $\begin{array}{l}\left|r+2\right|>6\\ r+2<-6\text{or}r+2>6\\ r+2-2<-6-2\text{or}r+2-2>6-2\\ r<-8\text{or}r>4\\ n\in \left(-\infty ,-8\right)\text{or}\left(4,\infty \right)\end{array}$

Thus, the solution set is $n\in \left(-\infty ,-8\right)\text{or}\left(4,\infty \right)$ .

Graph of the solution set is shown below: