Chapter EP, Problem 1.6.3EP

To determine

To Find: The absolute value of the inequality for the given condition and the graph the solution on the number line.

Answer to Problem 1.6.3EP

Therequired inequality is $\left|x\right|\le 2$ and the graph is shown in Figure

Explanation of Solution

Given:

The given statement is that all the numbers greater than or equal to $-2$ and less than or equal to $2$ .

Calculation:

Consider the absolute value of $x$ is,

  $\left|x\right|=\{\begin{array}{l}x,\text{if}x\ge 0\\ -x,\text{if}x<0\end{array}$

The statement that all the numbers greater than or equal to $-2$ and less than or equal to $2$ is expressed in equality as $\left|x\right|\le 2$ and in the form of inequality is,

  $-2\le x\le 2$

Thus, the required inequality is $\left|x\right|\le 2$ .

The graph of the inequality on the number line is shown in Figure 1

Figure 1