Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 31

$(0$, infinity)

$\frac{x}{x-10} < 0$ Denominator is zero when $x=10$ $x/(x-10) =0$ $x*(x-10)/(x-10) =0*(x-10)$ $x = 0$ (-infinity, $0)$ $(0$, infinity) Let $x=-1$, $x=1$ $x=-1$ $\frac{x}{x-10} < 0$ $\frac{-1}{-1-10} < 0$ $-1 /-11 <0$ $1/11 < 0$ (false) $x=1$ $\frac{x}{x-10} < 0$ $\frac{1}{1-10} < 0$ $1/-9 < 0$ $-1/9 < 0$ (true)