Question

Solve the following inequality:
$x^2-|5x-3|-x<2$

Answer 1

$x^2-|5x-3|-x<2$

$x^2-x-2<|5x-3|$

$|5x-3|>x^2-x-2$

$5x-3>x^2-x-2$ or $5x-3>-(x^2-x-2)$

$x^2-6x+1<0$

$(x-\frac{6+\sqrt{32}}{2})(x-\frac{6-\sqrt{32}}{2})<0$

$x-5.828\left)\right(x-0.172)<0$

$x\in (0.172,5.828)$

OR

$x^2+4x-5>0$

$x^2+5x-x-5>0$

$(x-1)(x+5)>0$

$x\in (-\infty ,-5)\cup (1,\infty )$

$\therefore x\in (-\infty ,-5)\cup (0.172,\infty )$