|x-|x-1||= floor(x)

Question

I am confused on how to find the answer of all x that fit into this equation and write it into interval notation.

Answer 1

If x>=1, left side=1, floor(x)=1, you get 1=<x<2

If 1/2=<x<1, left side=2x-1, floor(x)=0,so x=1/2

If x<1/2, left side=1-2x, floor(x)=1-2x, no solution