I have the following equation as a question for homework: $\lfloor 2x \rfloor = 2\lfloor x\rfloor$
I know what the solution is by deducting to the possibilities. Meaning this equation is true for any x which is between n (an integer) and $n+y$ where $0\leq y < \frac{1}{2}$
putting it simple: \begin{align} x \in \lbrace n + y | n \in \mathbb{Z} , y \in [0, 0.5) \rbrace \end{align} I just don't know how to algebraically get to this solution. Help will be appreciated!