The reverse Triangle Inequality states that $|a-b|\geq ||a|-|b||$ for any $a,b\in \mathbb R$. What about $|a-b-c|\geq ||a|-|b|-|c|| \tag{*}$ I know you will say its so elementary question, but I want to be sure:
So, repeating the original inequality for two numbers we get
$|(a-b)-c|\geq \big||a-b|-|c|\big|\geq \bigg|\big||a|-|b|\big|-|c|\bigg|$
should we have $|a|\geq |b|$ to get the required inequality in $(*)$?