Question

Solve the following inequality:
$\frac{|x+2|-x}{x}<2$

Answer 1

$\left(i\right)when(x+2)>0$

$x>-2$

$\frac{x+2-x}{x}-2<0$

$\frac{2-2x}{x}<0$

$\frac{x-1}{x}>0$

$x\epsilon (-\infty ,0)\bigcup (1,\infty )$

$sincex>-2$

$x\epsilon (-2,0)\bigcup (1,\infty )$

$\left(i\right)when(x+2)<0$

$x<-2$

$\frac{-x-2-x}{x}-2<0$

$\frac{-2-2x-2x}{x}<0$

$\frac{-2(2x+1)}{x}<0$

$\frac{x+\frac{1}{2}}{x}<0$

$x\epsilon (-\infty ,\frac{-1}{2})\bigcup (0,\infty )$

$x<-2$

$x\epsilon (-\infty ,-2)$

$x\epsilon (-\infty ,-2)\bigcup (-2,0)\bigcup (1,\infty )$