Question

Solve the following inequality:
$\sqrt{11-5x}>x-1.$

Answer 1

$11-5x\ge 0$

$5x-11\le 0$

$xϵ(-\infty ,\frac{11}{5}]$

$\sqrt{11-5x}>x-1$

Squarring both sides

$11-5x>x^2-2x+1$

$x^2+3x-10<0$

$(x+5)(x-2)<0$

$xϵ(-5,2)$

$xϵ(-5,\frac{11}{5}]$