Well it looks as if your only option is to install sliding panels as you will be needing access. Something easy to paint afterwards.
It's not easy to see other possibilities without physically being in the room.

Don't know if there are codes that would come into play here better ask a pro what is OK to do.

How big is your space -- full basement or partial basement or back of garage?

Do wires and pipes prevent you from putting a ceiling in the part of the basement that will be your laundry room?

Are you going to need room for a sump pump or other equipment?

Will you need a tool room for that tool box and/or could you build in shelves into the equipment side of the wall for tools?

If nothing else, a temporary "blind" could be a "wall" of thick black plastic sheeting with the vertical panels overlapping a few inches but leaving at least one space between two of the panels where the vertical panels are not taped together -- where it would be practical to put a door later -- so you could, as you need to, pass through the sheeting to get to the equipment and tools. I don't see how that could violate any code as long as you don't put a staple into a wire hanging it.

A temporary wall of plastic sheeting could, hopefully, later be the location of an actual floor to ceiling wall, or, if pipes and wires are in the way of putting up a ceiling, at least identify where you'd need later to place movable shelving units (about head high?) -- made with heavy plywood, and deep and wide enough to not topple over -- as a room divider (or perhaps two narrower "bookshelves" affixed back to back for storage shelves facing both the laundry and the equipment room).

Once you've defined the two areas, you can better see what space you have left with which to work.

Edit to add: Just noticed the date; hope you worked it out.

Thanks for the advice ...all

done !