# Chapter 9 - Inequalities and Problem Solving - Review Exercises: Chapter 9: 38

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To find all $x$ such that $f(x) \lt0 ,$ with $f(x)= |8x-3| ,$ solve the inequality \begin{array}{l}\require{cancel} |8x-3|\lt0 .\end{array} $\bf{\text{Solution Details:}}$ The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0.$ Since it is a distance, then $|x|$ is a nonnegative number. In the same way, the left side of the inequality, $|8x-3|\lt0,$ is always a nonnegative integer for any value of $n.$ This will never be less than the value at the right side. Hence, there is no solution.

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