I'm using a 2500 watt inverter with a regular car battery to power a vacation house with no city electricity or water, all my appliances work just fine except the water pump, the manual of the pump says 1500 watts at start and 750 watts afterwards, my fridge works fine, even the vacuum cleaner with 2000 watts works fine but as soon as I plug in the water pump the inverter cuts off, any advice on how to get the pump working would be appreciated,
The fridge motor is probably smaller than you think, the vacuum motor is a universal (AC/DC) motor so it inherently soft starts. The pump motor is likely a standard AC single phase motor and has too much inrush current for your inverter. When they say 1500W at start and 750W running, that's "marketing" speak because they don't want to scare people off. Starting an AC motor results in the inrush current being 500-600% of FLC for a second or two. But the power factor is very very low (i.e. .2 or less), so if you express it in "watts" the number looks better because W = A x V x PF. So 750W is about 1HP and at 115V single phase, that's about 16A FLC. That means at startup it can surge to 96A, but if the PF is 0.13, the W will be 1500 which LOOKS better than saying the starting current is 96A. For a utility connection it's irrelevant but for something powered by an inverter, it's too much and the inverter has a crowbar circuit that shuts it down to avoid damaging the transistors. Your best option (besides the generator one) quite honestly is going to be to get a different pump, either one powered by a DC motor that you run directly off of the battery (look for "solar pumps") or one that uses it's own inverter because that will come with soft starting. Or get a MUCH bigger inverter.
An inverter takes energy stored in the battery and changes it to higher voltage. A large car battery might store 50 ampere-hours, meaning it could provide about 5 amps for 10 hours, 20 amps for about 2 hours, or 200 amps, the draw of the inverter, for perhaps 5 minutes... note that the battery becomes much less efficient at higher current due to internal losses.
Your 2,500 W inverter is not the issue; it's the amount of electricity the battery can provide. Ten car batteries in parallel, using heavy wires, might run the inverter using a lot of appliances for two hours... and then you'd need to recharge all the batteries. As Heinlein stated, TANSTAAFL. This is obviously not a practical idea.