Chapter 5.5, Problem 48PFA

To determine

To solve the given compound inequality and to identify Reggie’s graph.

Answer to Problem 48PFA

The solution is $n\in \left(-\infty ,-3\right)\cup \left(-1,\infty \right)$ and the graph is,

  

Option D is correct.

Explanation of Solution

Given:

  $\left|2n+4\right|>2$

Calculation:

  $\begin{array}{l}\left|2n+4\right|>2\\ \Rightarrow 2n+4<-2\text{or}2n+4>2\\ \Rightarrow 2n<-2-4\text{or}2n>2-4\\ \Rightarrow 2n<-6\text{or}2n>-2\\ \Rightarrow n<\frac{-6}{2}\text{or}n>\frac{-2}{2}\\ \Rightarrow n<-3\text{or}n>-1\\ \Rightarrow n\in \left(-\infty ,-3\right)\text{or}n\in \left(-1,\infty \right)\\ \Rightarrow n\in \left(-\infty ,-3\right)\cup \left(-1,\infty \right)\end{array}$

Now the graph is,

  

Hence option D is correct.