I think that’s a bit off. You do need a lot of batteries to run a 2000 watt inverter for any amount of time.
Batteries don’t store watts, they store watt hours. A 2000 watt inverter run for 6 minutes uses 200 watt hours. So, part of the eqation would be you’d need at least 200 watt hours stored in your batteries.
Add to that, you don’t want to discharge your batteries below a certain percentage, so let’s say that’s a lead acid battery, which is 50%.
Another part is the battery has to handle the amps being put out by the inverter, which probably won’t be a factor with a couple of batteries.
A 6 volt golf cart battery holds around 200 amp hours of energy, or 1200 watt hours of energy, 600 watt hours usable. So that battery will run that inverter for 18 minutes.
Of course you won’t have a single 6 volt battery, you’ll have two in series for 12 volts, and now you have about 2400 watt hours of energy, or 1200 watt hours usable, and now you can run that inverter at 2000 watts for 36 minutes before your battery gets to 50%.
If you’re using lead acid and pulling that much energy, there’s a Puekert effect, which is like going heavy on the gaS where you burn more gas to go just as far. So the battery will get to 50% a bit earlier than 36 minutes.
But if you want to add solar panels in the daytime, you can use this free energy, but you can’t put too many panels on or they will push too much power to the battery.
For my lead acid batteries, that is about 13% of the pack or about 25 amp for the two batteries I mentioned. 25 amp hours is maybe 300 watts, which still means your inverter is pulling from the batteries 1700 watts.
With lithium you can charge the batteries at 50% so about 100 amps or 1200 watts, so even though the panels are pushing a lot more energy, you’re still short 800 watts that come from the batteries.