Chapter 1.6, Problem 7CYU

To determine

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

Answer to Problem 7CYU

The solution is given by $-6<z<6$ .

Explanation of Solution

Given information:

Given inequality

  $\left|z\right|<6$

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

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

Calculation:

Consider the given inequality,

  $\left|z\right|<6$

Now, solve the inequality as shown,

  $\begin{array}{c}\left|z\right|<6\\ -6<z<6\end{array}$

Hence, the solution of the inequality is $-6<z<6$ .

Now, graph the inequality as shown:

The open ball suggests that the solution region is not included the points $-6$ and $6$ .

The sign indicates the region is left side to the point $6$ and right side to the point $-6$ on number line.