Answer
$(−∞,-4)$ U $(5,∞)$
Work Step by Step
$(x-5)/(x+4) \ge 0$
The denominator is zero when $x=-4$, and the numerator is zero when $x=5$.
We have three sections: $(−∞,-4)$, $(-4, 5)$, and $(5,∞)$. We need to test one value for x in each section to determine if the section would be a solution set. Since we have the $\ge$ sign, we include the end points and use brackets instead of parentheses.
Let $x=-10$, $x=0$, and $x=10$
$x=-10$
$(x-5)/(x+4) \ge 0$
$(-10-5)/(-10+4) \ge 0$
$-15/-6 \ge 0$
$5/2 \ge 0$ (true)
$x=0$
$(x-5)/(x+4) \ge 0$
$(0-5)/(0+4) \ge 0$
$-5/4 \ge 0$ (false)
$x=10$
$(x-5)/(x+4) \ge 0$
$(10-5)/(10+4) \ge 0$
$5/14 \ge 0$ (true)
