## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 113

#### Answer

set of all real numbers

#### Work Step by Step

The given inequality, $|x-2|+3\ge2 ,$ is equivalent to \begin{array}{l}\require{cancel} |x-2|\ge2-3 \\\\ |x-2|\ge-1 .\end{array} For any $x$, the left side of the inequality above is a nonnegative number. This is always greater than the negative number at the right. Hence, the solution is the $\text{ set of all real numbers .}$

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