Question

A phrase describing a set of real numbers is given. Express the phase as an inequality involving an absolute value.

All real numbers x less than 3 units from 0

Short answer

$\left|x\right|<3$

Step-by-step solution

Step 1. The inequalities for the respective phrases.

The inequality for the phrase all real numbers x less than a units fromb is$\left|x-b\right|>a$

Step 2. Given phrase.

Given phrase is all real numbers less than 3 units from 0

Step 3. Writing the Inequality.

So, the inequality for the phrase is

$\begin{array}{c}|x-0|<3\\ or,\left|x\right|<3\end{array}$