Chapter 2.1, Problem 6QR

To determine

Towrite:The inequality $\left|x\right|<c^2$ in the form of $a<x<b$ .

Answer to Problem 6QR

The inequality $\left|x\right|<c^2$ in the form of $a<x<b$ is written as $-c^2<x<c^2$ .

Explanation of Solution

Given information:

The inequality is $\left|x\right|<c^2$ .

Calculation:

If a modulus of a variable is less than a positive number $a$ , then the variable lies between $-a$ and $a$ .

  $\begin{array}{c}\left|x\right|<a\\ -a<x<a\end{array}$

Substitute $c^2$ for $a$ in the above inequality.

  $\begin{array}{c}\left|x\right|<c^2\\ -c^2<x<c^2\end{array}$

Therefore, the inequality $\left|x\right|<c^2$ in the form of $a<x<b$ is written as $-c^2<x<c^2$ .