Is it possible to lay carpet padding and carpet over a concrete slab floor?
yup you can and should get the old carpet out, it is possible I’ve had to do it many times. Scrape it, pull it whatever it takes. When you put the new carpet in I’d suggest not gluing it down unless it is a level loop carpet. If you use a plush or a berber they make tack strip for concrete. The only other suggestion I can make for this is to use 2 pieces of tack strip instead of one. Two gives you much better holding power and keeps the carpet from wrinkling over time. Install the tack strip as normal then just add another piece in front of it. You would still have to fasten the plywood to the floor or it would warp and your carpet will look like a putting green.