Running A/C off a 12vdc inverter is going to generate a lot of heat, especially if the compressor is constantly engaged. 2500w inverter and 400ah (4.8kwh) of battery bank and would never consider running A/C off the batts - ever.
Get the skinny. Try posting your question here in Beginner's Corner:
https://diysolarforum.com. You'll get an answer. Consider a soft start if you still plan to continue down that road. I have a feeling their knowledge will change your mind.
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