Chapter 1.6, Problem 17PPS

To determine

To solve: the given inequality and graph the solution on number line.

Answer to Problem 17PPS

The solution is given by $k<-4\text{or}k>4$ .

Explanation of Solution

Given information:

Given inequality

  $\left|-4k\right|>16$

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

More over

  $\begin{array}{l}\left|x+a\right|>b\\ \Rightarrow x+a>borx+a<-b\end{array}$

Calculation:

Consider the given inequality,

  $\left|-4k\right|>16$

Now, solve the inequality as shown,

  $\begin{array}{c}\left|-4k\right|>16\\ -4k>16\text{or}-4k<-16\\ 4k<-16\text{or}4k>16\\ k<-4\text{or}k>4\end{array}$

Hence, the solution of the inequality is $k<-4\text{or}k>4$ .

Now, graph the inequality as shown:

The open ball suggests that the solution region is not included the points $-4$ and $4$ .

The sign indicates the region is left side to the point $-4$ and right side to the point $4$ on number line.