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

$x$ 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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