Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 38

(-infinity, $3)$

$(x-3)/(x+2) \leq0$ Denominator is zero when $x=-2$ $(x-3)/(x+2) \leq0$ $(x-3)/(x+2) =0$ $(x-3)*(x+2)/(x+2) =0*(x+2)$ $x-3=0$ $x=3$ (-infinity, $3)$ $(3$, infinity) Let $x=0$ and $x=5$ $x=0$ $(x-3)/(x+2) \leq0$ $(0-3)/(0+2) \leq0$ $-3/2 \leq 0$ (true) $x=5$ $(x-3)/(x+2) \leq0$ $(5-3)/(5+2) \leq0$ $2/7 \leq 0$ (false)