$$\frac{2x+5}{x-5}\ge-3$$
$x\in (-\infty,2]\cup (5,\infty)$
$$x-5>0$$ $$x-5<0$$
$$x>5$$
$$2x+5\geq -3\left(x-5\right)$$
$$2x+5\geq -3x+15$$
$$2x+3x\geq -5+15$$
$$5x\geq 10$$
$$x\geq 2$$
$$x<5$$
$$2x+5\leq -3\left(x-5\right)$$
$$2x+5\leq -3x+15$$
$$2x+3x\leq -5+15$$
$$5x\leq 10$$
$$x\leq 2$$
$$x\in (-\infty,2]\cup (5,\infty)$$
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