jmc

We can superimpose the graph of $y=1.8$ on the same axes as the original graph:



There are three intersections. The leftmost intersection lies on the line of slope $2$ through the origin, which is $y=2x$. Solving $2x=1.8$ yields $x=0.9$.

The middle intersection lies on the line of slope $-1$ through $(2,1)$, which is $y=-x+3$. Solving $-x+3=1.8$ yields $x=1.2$.

The rightmost intersection lies on the line of slope $2$ through $(2,1)$, which is $y=2x-3$. Solving $2x-3=1.8$ yields $x=2.4$.

Thus, the sum of the three $x$-coordinates is $0.9+1.2+2.4=\boxed{4.5}$.