Question

Solve the following inequality:
$\frac{5x+8}{4-x}<2$

Answer 1

$\frac{5x+8}{4-x}<2$

$\frac{5x+8}{4-x}-2<0$

$\frac{5x+8-2(4-x)}{4-x}<0$

$\frac{5x+8-8+2x}{-(x-4)}<0$

$\frac{7x}{x-4}>0$

$\frac{x}{x-4}>0$

$\frac{(x-0)}{(x-4)}>0(x=1,\frac{1}{-3}<0)$

$x\epsilon (-\infty ,0)\bigcup (4,\infty )$