Answer
All real numbers except $-\frac{1}{3}$.
Work Step by Step
We are given:
$|\displaystyle \frac{x-4}{3x+1}|\geq 0$
We can see right away that this equation is almost always true because an absolute value is always positive or 0:
$|x|\geq0$ for all $x$
However, if the denominator is zero we will get an undefined value. Thus this solution must be removed:
$3x+1\ne0$
$x\ne -\frac{1}{3}$
Therefore, the solution is all real numbers except $-\frac{1}{3}$.
