Chapter 12, Problem 73CLR

To determine

To graph: The solution set of the given inequality.

Answer to Problem 73CLR

The graph is shown in Figure 1.

Explanation of Solution

Given:

The inequality is $\left|x+1\right|>3$ .

Calculation:

For an equation of the form $\left|x\right|>n$ , it can be broken into 2 inequalities- $x>n$ and $x<-n$ .

So, from $\left|x+1\right|>3$ , two inequalities obtained are $x+1>3$ or $x+1<-3$ .

From $x+1>3$ ,

  $\begin{array}{c}x+1-1>3-1\left[\text{Subtracting }1\text{ from both sides}\right]\\ x>2\end{array}$

From $x+1<-3$ ,

  $\begin{array}{c}x+1-1<-3-1\left[\text{Subtracting }1\text{ from both sides}\right]\\ x<-4\end{array}$

So the solution becomes $\left(-\infty ,-4\right)\cup \left(2,\infty \right)$

and is plotted in the graph as shown below:

  

Figure 1