In Sipser's book of Theory of Computation, related to Reducibility, it's written
if A is undecidable and reducible to B, B is undecidable.
The confusion is, only a solution to B determines a solution to A, if i'm not wrong. So, for instance if B is decidable and A is undecidable, what does it mean? Here B isn't undecidable.
Hope you got it.