Should I continue to use my old M11x laptop battery?

My Dell M11x laptop battery had very little life left and would only run for about 20 minutes when unplugged from the adaptor. I purchased a new M11x battery, but seeing as I usually use my laptop plugged into the adaptor, should I save this new battery for periods when I know I won't be able to be plugged in?

yes. Just remember to do standard battery mainteneance. That is at least once per 6 months run on that battery until the laptop shuts down (to make sure it's fully discharged) then recharge it fully. Don't keep that battery in places too cold or too hot to live in.

You can try the same on the "old" battery and see if there is any improvement. As batteries last as much as their controller thinks they will last based on usage or whatever, and this procedure resets the controller to real battery capacity.