If you have unsightly brush marks left over from a bad paint job on walls, take heart. You have two ways to eliminate them.
Try sanding first to see if that will work. Use 80-grit sandpaper on either a sanding pole or a sanding block (Photo 1). Use a “clog resistant” type, such as 3M Sandblaster sandpaper, or wipe the sandpaper often with a stiff brush to keep it from clogging up. Avoid the temptation to use an electric sander to make the job go faster. It'll heat up the paint and cause it to get gooey rather than sand away the brushstrokes.
If sanding doesn't work or the entire wall has brush marks, save yourself time and effort by applying a thin coat of topping joint compound over the walls using a 12-in. drywall taping knife—a process called skim coating (Photo 2). Then smooth out with 100-grit sandpaper any rough spots in the skim coat, apply a coat of primer and paint the walls. Skim coating ensures that you'll end up with a (nearly) perfectly smooth wall.