Chapter 1.6, Problem 8CYU

To determine

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

Answer to Problem 8CYU

The inequality has no solution.

Explanation of Solution

Given information:

Given inequality

  $\left|x\right|\le -4$

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

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

Calculation:

Consider the given inequality,

  $\left|x\right|\le -4$

Now, solve the inequality as shown,

  $\left|x\right|\le -4$

Absolute value of any number cannot be negative.

So, the inequality has no solution.