College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 166: 123


$(-\infty, \infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |4x-12|\ge-3 ,$ use the definition of absolute value to analyze the given inequality. $\bf{\text{Solution Details:}}$ The absolute value of $x$, given by $|x|,$ is the distance of $x$ from $0,$ and hence is always a nonnegative number. Therefore, for any $x,$ the expression at the left, $ |4x-12| ,$ is nonnegative. This is always greater than or equal to the negative expression at the right. Hence, the solution set is the set of all real numbers or the interval $ (-\infty, \infty) .$
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