Question

In a Rational inequality when do you have to change the sign of the inequality?

Answer 1

Rewrite as $x^3-x^2 \geq 0$. The roots of the corresponding equation are x=0 and x=1.


The tricky part is reading off all solutions: Clearly, the numbers in the interval $[1,\infty)$ are solutions, but don't forget x=0. (Check that x=0 is indeed a solution!) Thus the set of solutions is the following set:

\begin{displaymath}\{0\}\cup [1,\infty).\end{displaymath}