Looking at the 1881 sheet, Alex and Sarah are down as being born Salford. Joseph was born Cheltenham and Hugh Bollington.
Joseph and Hugh's births, though, were registered in Salford.
I think that the enumerator mistranscribed the original places of birth, which would make the Cheltenham area Alex's birthplace.
Slymansdale, though, does not seem the right style of placename for the area around Cheltenham. The town itself is in the flattish area around the Severn, and the hills to the south east seem to have -combe names rather than -dale.
My guess is that Alexander moved around as a child, so may not have known where he was actually born. One of my relatives keeps changing her place of birth at censuses. Sometimes she says Manchester, sometimes St Helens (where she was as a teenager), a couple of time "Bradbury". I now think that I've found her in 1841 as a child at Cleobury Mortimer in Shropshire.
