Is it always true? $\left|A-B\right| \le \left|A\right| + \left|B\right|$

Question

Is it always right to claim that: $$\left|A - B\right| \le \left|A\right| + \left|B\right|$$

where $A, B \in \mathbb{R}$ ?

Answer 1

Yes. $$|A-B|=|A+(-B)|\le|A|+|-B|=|A|+|B|.$$

Answer 2

Triangle inequality in one-dimension.

Answer 3

Hint:

Consider the cases where both $A$ and $B$ are either negative or positive (you should get an inequality)

Consider then the cases where one of them is negative and the other positive (you should get an equality)

(The cases where one or both are zero are trivial)