College Algebra (11th Edition)

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

Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises - Page 154: 24

Answer

$x$ cannot have a negative solution

Work Step by Step

The absolute value of $x$, written as $|x|,$ is the distance of $x$ to $0,$ and hence, is always a nonnegative number. In the same reason, for any $x,$ the left side of the given equation, $ |5x-6| ,$ is always a nonnegative number. Therefore, the value of $x$ in the right-hand expression should also be a nonnegative number so that $ 3x $ is nonnegative. That is, $x$ cannot have a negative solution.
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