Airport express as an intension to motorola wireless modem

My house is REALLY long and lots of walls. When we built it I put ethernet in a couple of the rooms that were probably going to have computers. I now have a wireless network (Motorola Modem) through ATT DSL. I run three computers close to the modem, however I now want to run AppleTV to a library at the other end of the hall. Can I use the Airport express with an ethernet cable to the HDMI TV?

I would probably have to run a ethernet cable to the modem also.

Is it possible to do this?

Thanks

Anita