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 more than 2 units from 0

Short answer

$\left|x\right|>2$

Step-by-step solution

Step 1. The inequalities for the respective phrases.

The inequality for the phrase all real numbersx more than a units from b is $|x-b|>a$.

Step 2. Given phrase.

Given phrase is all real numbers more than 2 units from 0

Step 3. Writing the Inequality.

So, the inequality for the phrase is

$\begin{array}{c}|x-0|>2\\ \mathrm{or},\left|x\right|>2\end{array}$