Great question — answering as the UphillTech team:
Removing popcorn is usually easy to do, ( but very messy) by wetting with a spray and scraping off. However yours is painted and that will not work. As others said you could cover with 1/4" drywall. That could cause problems with door trim and screw up dimensions and such. What I have done is skim over the surface with drywall compound, then spray on a more modern texture like orange-peel. Prime and paint when dry. The process is simple. Using an 8 or 10 inch drywall knife spread compound, (I like using "all purpose") on the wall starting with the bottom and applying it moving up to about mid wall, then from the ceiling down. This leaves only a line near the middle and a slight line between...
Full answer by RMDman: https://diy.stackexchange.com/a/317044 (CC BY-SA 4.0).
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