Question

Find range of $x$

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

Answer 1

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

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

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

$\left(\frac{7x}{4-x}\right)<0$

$\therefore x\in (-\infty ,0)\cup (4,\infty )$