Browsing through the inequalities tag, I see a lot of straightforward-looking arithmetic statements that I nevertheless have no idea how to prove (and apparently I'm not alone). With equalities it's usually clear what is required: A sequence of clever arithmetic manipulations until at last one arrives at a tautology. With inequalities, I often find myself not even knowing where to start.
Is this true in general, or do I simply not know the right techniques to apply here?