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: 25


$x$ cannot have a positive 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, $ |7x+3| ,$ is always a nonnegative number. Therefore, the value of $x$ in the right-hand expression should be nonpositive so that $ -5x $ is nonnegative. That is, $x$ cannot have a positive solution.
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