Chapter A, Problem 34E

To determine

To solve: The inequality.

Answer to Problem 34E

The interval notation for the given inequality is $\left(-\infty ,-3\right]\cup \left[3,\infty \right)$.

Explanation of Solution

Given:

The inequality is $\left|x\right|\ge 3$.

Property used:

$\text{If }\left|x\right|=a\text{ if and only if }x=\pm a$

$\text{If }\left|x\right|>a\text{ if and only if }x>a\text{ and }x<-a$

Calculation:

By the property mentioned above, the given function can be re written as,

$\begin{array}{l}\left|x\right|\ge 3\\ x\le -3\text{ or }x\ge 3\end{array}$

The corresponding interval notation is $\left(-\infty ,-3\right]\cup \left[3,\infty \right)$.

Thus, the interval notation for the given inequality is $\left(-\infty ,-3\right]\cup \left[3,\infty \right)$.