Inspiron 15-3521 used on modified sine wave inverter

You will need the AC adapter to charge the battery.  A DC power supply converter (not inverter) won't charge the battery.

You are better off with a pure sine wave inverter - as long as it can supply the power requirements of the adapter (90W or better) it should work fine.

Will the inverter charge the battery ok? I don't need to run laptop continually on inverter power.

I know I need to use the AC adapter. I am asking if it will charge the batteries ok plugged into a modified sine wave inverter?

It should, assuming the inverter can power the adapter.  A pure sine wave inverter as noted, though is a better idea.