I am wondering if someone can provide some geometric intuition, or some simple way to visualize why $$ c-d<a-b \implies b<a+d-c $$

The way I have been trying to do this is to think of $a,b,c,d$ as points in $\mathbb{R}$ and $a-b, c-d$ as the space between them. but

- $c-d<a-b$ doesn't necessarily mean that $\vert c-d\vert < \vert a-b\vert$,
- and when rearranged to be $b<a+d-c$, the left hand side is no longer a "space between two points"

So my approach didn't really help me.