Geometric argument to solve $|x-1|<|x+1|$

Question

I am trying to solve the inequality $$|x-1|<|x+1|$$ using geometry. In general, I know that $|x-c|$ for $x,c\in\mathbb{R}$ can be thought of as the distance from $x$ to $c$. This is easy to view on a number line. However, I am unsure of how to solve the problem at hand using a similar argument. Any advice is appreciated.

Answer 1

I'm not sure why this was originally answered in comment form, but to cut down on the number of unanswered questions, I'll answer now. The inequality means that the distance between $x$ and $1$ is less than the distance between $x$ and $-1$. You've correctly concluded that this is equivalent to the inequality $x>0$.