Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 29

(-infinity, $0)$ U $(1$, infinity)

$x^2 > x$ $x^2-x > x-x$ $x^2-x > 0$ $x(x-1) > 0$ $x=0$ $x-1 = 0$ $x=1$ (-infinity, $0)$ $(0,1)$ $(1$, infinity) Let $x=-2$, $x=1/2$, $x=10$ $x=-2$ $x^2 > x$ $(-2)^2 > (-2)$ $4 > -2$ (true) $x=1/2$ $x^2 > x$ $(1/2)^2 > 1/2$ $1/4 > 1/2$ (false) $x=10$ $x^2 > x$ $10^2 > 10$ $100 > 10$ (true)