Do all bacteria have both a cell wall and a membrane?

Not all bacteria but some bacteria have both a cell wall and a cell membrane... all those with a cell wall contain a cell membrane. *

Yes, all bacteria have both an outer cell wall and, below it, a membrane that surrounds the cytoplasm. At one time scientists thought that some bacteria (the gram-negative ones) lacked a wall, but it turned out that there was a thin peptidoglycan layer.