Chapter 6.6, Problem 38HP

To determine

To find:A system of inequalities equivalent to $\left|x\right|\le 4$ .

Answer to Problem 38HP

  $\begin{array}{l}x\ge -4\\ x\le 4\end{array}$ .

Explanation of Solution

Given information:

  $\left|x\right|\le 4$

On the Number line $\left|x-a\right|\le b$ represents all the points whose distance from the point $a$ is less than or equal to $b$ .

  $\Rightarrow -b\le x-a\le b$

  $\Rightarrow -b+a\le x\le b+a$

  $\left|x\right|\le 4$

Here as $a$ is 0 it means distance from origin and $b$ is 4

Therefore from above concept

We get

  $-4\le x\le 4$

This can be written as

  $-4\le x$ and $x\le 4$

  $x\ge -4$ and $x\le 4$ .

Therefore

System of inequalities which represent given situation are

  $\begin{array}{l}x\ge -4\\ x\le 4\end{array}$