APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 35

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

$x^3 \gt x$ Case 1: $x \lt 0$ $x^3 \gt x$ $x^2 \lt 1$ $\vert x \vert \lt 1$ $-1 \lt x \lt 0$ Case 2: $x \gt 0$ $x^3 \gt x$ $x^2 \gt 1$ $x \gt 1$ Solution: $-1 \lt x \lt 0~~~$ or $~~~x \gt 1$ The solution set is $~~~(-1, 0) \cup (1, \infty)$