Chapter 11 - Section 11.4 - Nonlinear Inequalities in One Variable - Exercise Set - Page 799: 37

$(5$, infinity)

$(x-5)/(x+4) \geq0$ Denominator is zero when $x=-4$ $(x-5)/(x+4) \geq0$ $(x-5)/(x+4) =0$ $(x-5)*(x+4)/(x+4) =0*(x+4)$ $x-5=0$ $x=5$ (-infinity, $5)$ $(5$, infinity) Let $x=0$ and $x=10$ $x=0$ $(x-5)/(x+4) \geq0$ $(0-5)/(0+4) \geq0$ $-5/4 \geq 0$ (false) $x=10$ $(x-5)/(x+4) \geq0$ $(10-5)/(10+4) \geq0$ $5/14 \geq 0$ (true)