Question

Solve the following inequality:
$\frac{|x+2|-|x|}{\sqrt{4-x^3}}⩾0$

Answer 1

$\frac{|x+2|-\left|x\right|}{\sqrt{4-x^3}}\ge 0\sqrt{4-x^3}>04-x^3>0x<2\sqrt{2}x\le -2\frac{-x-2-(-x)}{-2\ge 0}\ge 00\ge x\ge -2x+2-(-x)\ge 02x\ge -2x\ge -1x\in [-2,-1]x>0x+2-x\ge 02\ge x\in (0,2\sqrt{2})x\in (-2,-1)\text{U}(0,2\sqrt{2})$