Chapter 1.6, Problem 6E

To determine

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

Answer to Problem 6E

The solution is given by $q\ge -1\text{or}q\le 1$ .

Explanation of Solution

Given information:

Given inequality

  $\left|q\right|\ge -1$

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

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

Calculation:

Consider the given inequality,

  $\left|q\right|\ge -1$

Now, solve the inequality as shown,

  $\begin{array}{c}\left|q\right|\ge -1\\ q\ge -1\text{or}q\le 1\end{array}$

Hence, the solution of the inequality is $q\ge -1\text{or}q\le 1$ .

Now, graph the inequality as shown:

  

The closed ball suggests that the solution region is included the points $-1$ and $1$ .

The sign indicates the region is left side to the point $1$ and right side to the point $-1$ on number line.