$\displaystyle x^3 >= 6x - x^2$
Where >= : less than or equal to ..
I am not sure at all about how to solve an inequality of this type but I can solve inequalities involving squares.
$\displaystyle x^3 \ge 6x - x^2$
x= 0 is an obvious answer
---------------------------------
If x>0
$\displaystyle x^3 \ge 6x - x^2$
$\displaystyle x^2 \ge 6 - x$
$\displaystyle x^2 +x - 6 \ge 0 $
$\displaystyle (x-2)(x+3) \ge 0 $
$\displaystyle x \ge 2 $ , both terms positive hence x>3 is an answer
$\displaystyle 2 > x > 0$ One of the term is negative hence
its not an answer
-----------------------------------
When x<0 , sign of inequality changes as , you can remember that we canceled an x initially
$\displaystyle 0 \le x \le -3 $, is an answer
$\displaystyle x< -3$ is similarly not an answer