#### Answer

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.