Question

Solve the following inequality:
$|x|<\frac{a}{x}$

Answer 1

$|x|<\frac{a}{x}⟹(x|x|-a)<0⟹x<0⟹-x^2-a<0⟹x^2+a>0⟹x\in (-\sqrt{-a},0)$ or $x>0⟹x^2-a<0⟹x\in (0,\sqrt{a})$