Quick Modulus question!

Hi, I just wanted to ask the best way of going about answering this modulus inequality. The squaring method didn't work for me and I'm not 100% sure exactly what the shape of the graph

$\ y = 2|x-1|$


actually looks like, in order to use the graphs method. Also, once I have done the graph and want to find the points of intersection, how do I find the point of intersection in the negative quadrant? Do I negate the graph $\ y = 2|x-1|$ and$\ y = |x-2|$ and does $\ -(2|x-1|) = -|x-2|$?? I'm slightly confused to be honest!!

The question is this...

Solve the inequality:

$\ 2|x-1| < |x-2|$

Thanks for your help!

Hi, I just wanted to ask the best way of going about answering this modulus inequality. The squaring method didn't work for me

Perhaps you should be asking why the squaring method didn't work - I suspect an arithmetic error. Worked fine when I did it. Post some working if you'd like someone to check what you've done.

For the $\ 2|x-1|$ part, do you square the entire thing ie. $\ (2|x-1|)^2$ or only what's in the modulus brackets? I'm not even sure I know how to square $\ (2|x-1|)^2$
if it is that!!