The inequality y+x<2(x-1)-x is first solved (simplified) and then graphed. 

 y+x<2(x-1)-x is equivalent to y < -2

And then y < -2 is graphed:

Since x can be any value, the solution is the open half-plane, the left side of the line y = -2.

The boundary line, y = -2, is not included in the required region.