Proof of an inequality with the triangle inequality

Question

How can I prove this inequality using the triangle inequality?

$|a-b| \leq |a-c| + |c-b|$

Possible duplicate of Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$ — Martin R, Mar 26 '18 at 20:47

score 1 · Accepted Answer · answered Mar 26 '18 at 19:51

1

$$|a-b|=|(a-c)+(c-b)|\leq |a-c|+|c-b|$$

answered Mar 26 '18 at 19:51

nonuser

score 1 · Answer 2 · answered Mar 26 '18 at 19:51

1

$$\vert (a-c)+(c-b) \vert = \vert a-b \vert \leq \vert a-c \vert + \vert c-b \vert$$

answered Mar 26 '18 at 19:51

Mario SOUPER

2 Answers2