Proving that: $ | a + b | + |a-b| \ge|a| + |b|$ I am trying to prove this for nearly an hour now:

$$
\tag{$\forall a,b \in \mathbb{R}$}| a + b |  + |a-b| \ge|a| + |b|
$$

I'm lost, could you guys give me a tip from where to start, or maybe show a good resource for beginners in proofs ? 
Thanks in advance.

Using triangle inequality,
$$|a+b| + |a-b| \geqslant |(a+b) + (a - b)| = 2|a|$$
also as $|a-b| = |b-a|$,
$$|a+b| + |a-b| \geqslant |(a+b) + (b - a)| = 2|b|$$
Now add and conclude!
