Question

Solve the following inequality:
$x>\sqrt{24-5x}.$

Answer 1

$24-5x\ge 0$

$x-\frac{24}{5}\le 0$

$xϵ(-\infty ,\frac{24}{5}]$

$x>\sqrt{24-5x}$

Squarring both sides

$x^2>24-5x$

$x^2+5x-24>0$

$(x+8)(x-3)>0$

$xϵ(-\infty ,-8)\cup (3,\infty )$

$xϵ(-\infty ,-8)$