How long would a fully charged 230AH 12V battery last when using it with a 12V->230V DC>AC inverter, drawing an average of 1500 watts power?
Say you draw 1700w due to inverter efficiency, which is 142Amps.
230Ah capacity is usually at 0.01C which means this is the capacity at (Battery Ah)*0.1 Amps Draw - which is 23Amps in your case.
If you go to 0.5C (115A) for example, your capacity is around 70%.
After understanding this, there are a few more things to be aware of:

On such amperage you are going to create a lot of heat, I don't think you want to run on such amperage for a long time. (Rule of thumb - don't let your battery get to 50C). Batteries that get warm while operating/in storage die very early
Lead Acid batteries should not be discharged to more than 50-70% (depending of their technology and quality) of their full capacity - on your case it means DO NOT discharge more than 115Ah! (This is called DoD, discharging more than this will shorten the life of your battery drastically)
This amperage requirs very thick cables, consider going to higher voltage batteries (in series) and inverter to lower the amperage