Proof of very simple absolute value inequality

Question

I was wondering how to prove this. It always appears to be true when I plug in values.

$a,b,c \in \mathbb{R}\\a\lt b\lt c$

Prove $\forall a,b,c : \left|a + b\right| \space\lt \left|a + c\right|$

Answer 1

This is false. $a = -100, b=-1$ and $c=1$.

Answer 2

It's false. Consider $a=-2$, $b=-1$, $c=0$, then $$3=|{-}2-1|\not<|-2+0|=2$$