Power inverter for portable ac

I’m looking for a temporary solution. My air conditioner went out so I’m in the process of acquiring all the stuff to replace the whole system. So in the meantime, I thought, hey I’ll run a small portable ac off my inverter. The portable ac works but does not stay on, meaning it will turn on, start cooling, but it draws too much on my inverter (might be a little tired) and I get the low voltage cut out on the inverter. Truck volts don’t drop at least from what I can tell. So I’m wondering if this is just impractical or if I had a more powerful inverter, could I get this to stay on.
Current inverter is a older cobra 1500w
Portable ac is a 5k btu, 870w input cooling power, cooling current 7.7a, L.R.A./R.L.A of compressor 35a/ 6.58a, F.L.A. Of fan .78a, rated current 8a.

small fridge and microwave is also run off the inverter. I would not use the ac and microwave at the same time.

I will only be using the portable ac while the truck is running/idling because I’m sure it would love to drain the batteries. Do y’all think a 3k inverter will do the job? Or?

 

That is not a bad idea and I will probably keep the ac unit afterwards and do this.

my immediate problem is with wanting to run the ac during the day so that’s why I was wanting to go the inverter route. Any idea if the inverter will run it as long as the truck is running.