I've got stuck on this problem
Let $a$, $b$, $c> 0$ and $x$ a real number such that $$|ax - b| \leq c,$$ $$|bx - c| \leq a$$ and $$ |cx - a| \leq b.$$
Prove that $0 \leq x \leq 2$.
What I've tried so far - to sum all three inequalities and to square the expresion. And the properties of modules of course ( such as $|x| + |y| >= |x+y| $) . It wasn't too helpful.
I would apreciate some hints.