Cheaper or not, isn’t a huge factor.

My really expensive sol-ark 12k cannot start my 110v air-compressor.

The issue is, the rated L.R.A. ie, locked rotor amps, how much current it takes to get it started.

My A/C motor, for example, uses around 20 amps @ 240v when running, ie ~5,000w. However, its L.R.A, is 112.0 amps @ 220v, ie- (24,640 watts). Which is more than the peak load my 12k inverter can handle. So- if you tried to start it on the inverter, well, it doesn’t work.

static.xtremeownage.com/blog/2023/off-grid-ac/

The same principle applies to anything with a motor.

You have to evaluate the L.R.A. Remember, if you have say, a 5,000watt RMS inverter, which can handle a 10k peak- its not going to be able to start something that has a 14,000 startup draw.