Hanging cabinets with 3/8" particle board backs

I picked up some salvage cabinets off of craigslist that I want to hang in our laundry room above the washing machine and dryer.

The cabinets were originally in a kitchen at the floor level and I’m concerned that they might be insufficiently sturdy to hang higher up and potentially have heavy things like liquids in them.

The backs of the cabinets are 3/8" veneered particle board. If I screw through that into a stud with a washer to spread the load, is that going to be strong enough? Or should I glue, say, a 1/4" sheet of plywood to the back of each cabinet before attaching to the wall to give it some more strength?

I’d screw a small furring strip (3/4 inch thick solid material, like a 1x2) into the studs and let the bottom of the cabinets rest on that to add support and strength. If I were going to run something through the particle board, I would do the same from the inside.

Instead of a washer, screw through a piece of 1x2 that runs the width (left to right) of the cabinet, along the top. That should add enough strength.

Ah, perfect, that makes sense. I was going to do the strip on the bottom for them to rest on, but the one inside is exactly the tip I needed.

I would use French cleats - attach a rail to the full width of the cabinet (so it can be affixed into the carcase as well as the backboard) - attach the other rail to the wall (allowing you to screw into studs at the right places) and then hang the cabinet on the cleats - with a couple of small screws through into the lower rail to prevent the cabinet being bumped off the cleat