Answer
$x \lt 0~~~$ or $~~~x \gt \frac{1}{4}$
The solution set is $~~~(-\infty, 0) \cup (\frac{1}{4}, \infty)$

Work Step by Step
$\frac{1}{x} \lt 4$
$0 \lt \frac{1}{x} \lt 4~~~$ or $~~~x \lt 0$
$x \gt \frac{1}{4}~~~$ or $~~~x \lt 0$
The solution set is $~~~(-\infty, 0) \cup (\frac{1}{4}, \infty)$
