APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 37

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

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