Answer
$[-3,2]$
Work Step by Step
We are given the inequality:
$6-x\geq x^2$
Rewrite the inequality:
$x^2+x-6\leq 0$
Factor:
$x^2-2x+3x-6\leq 0$
$x(x-2)+3(x-2)\leq 0$
$(x-2)(x+3)\leq 0$
Solve the two linear equations:
$x-2=0\Rightarrow x=2$
$x+3=0\Rightarrow x=-3$
The solution of the inequality is:
$[-3,2]$
