Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 798: 15

$(-7, 2)$

$(x+7)/(x-2)<0$ Denominator is zero when $x=2$ $x+7=0$ $x=-7$ (-infinity, $-7)$ $(-7, 2)$ $(2$, infinity) Let $x=-10$, $x=0$, $x=10$ $x=-10$ $(x+7)/(x-2)<0$ $(-10+7)/(-10-2)<0$ $-17/-12 < 0$ $17/12 < 0$ (false) $x=0$ $(x+7)/(x-2)<0$ $(0+7)/(0-2)<0$ $7/-2 <0$ $-7/2 < 0$ (true) $x=10$ $(x+7)/(x-2)<0$ $(10+7)/(10-2)<0$ $17/8 < 0$ (false)