Question

Solve the following inequalities.
$x+1<\sqrt{11-x}$

Answer 1

$x+1<\sqrt{11-x}$

For root to be defined, $11-x\ge 0⟹x\le 11$

Now,squaring both sides-

$x^2+2x+1<11-x$

$⟹x^2+3x-10<0$

$⟹(x+5)(x-2)<0$

$⟹-5<x<2$

Hence, solution set is $x\in (-5,2)$