Proof by cases, inequality I have the following exercise:

For all real numbers $x$, if $x^2 - 5x + 4 \ge 0$, then either $x \leq 1$ or $x \geq 4$. 

I need you to help me to identify the cases and explain to me how to resolve that. Don't resolve it for me please.

HINT:
If $(x-a)(x-b)\ge0$  
Now the product of two terms is $\ge0$
So, either both $\ge0$ or both $\le0$
Now in either case, find the intersection of the ranges of $x$
