## College Algebra (11th Edition)

Published by Pearson

# Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises: 56

#### Answer

$(-\infty,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the concepts of absolute value expressions to solve the given inequality, $|12-9x|\ge-12 .$ $\bf{\text{Solution Details:}}$ The absolute value of a number is the distance of the number from $0,$ and hence, is always a nonnegative number. In the same reason, for any $x$, the expression at the left side is always a nonnegative number. This will always be $\text{ greater than or equal to }$ the expression at the right. Hence, the solution is the set of all real numbers or $(-\infty,\infty) .$

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