TV watching with separate inverter?

 Okay so lets say we have 2 acid 12v batteries fully charged while dry camping in your new 2500RL 30 Amp rig.
Regardless if they are charged that day with a Solar set up or a handy Generator, this part doesn't really matter for the question.

What if I connect the TV to a seperate small inverter (behind the TV) and have the inverter pull power directly from the rig via plug outlet to power the tv.
The question is how long could someone watch TV in this manner? What small inverter would you recommend? 

How do I figure this out, can I do this without setting up a full inverter change on the rig? 
Oh and how would this "watch time" compare to 2 full charged 12v 100 Amp Lithium batteries at night?

Thank you in advance.
EXTREME the "Ultra Newbie"