Question

Solve the following inequality:
$\frac{3}{\sqrt{2-x}}-\sqrt{2-x}>2.$

Answer 1

$2-x\ge 0x\le 2x\in (-\infty ,2)\frac{3}{\sqrt{2-x}}-\sqrt{2-x}>2\frac{3-2+x}{\sqrt{2-x}}>2x+1>\sqrt[2]{22-x}{(x+1)}^2>4(2-x)x^2+2x+1>8-4x{x}^2-6x-7>0(x-7)(x+1)>0x\in (-\infty ,-1)\cup (7,\infty )x\in (-\infty ,-1)$