Is this equation about floor function correct?

Question

I am trying to solve this equation. Please correct me.

$$\lfloor{x}\rfloor + \lfloor{w} - \lfloor{x}\rfloor \rfloor=\lfloor{x}\rfloor-\lfloor{x}\rfloor+\lfloor{w}\rfloor$$

$$=\lfloor{w}\rfloor$$

Answer 1

If $k$ is an integer, then $\lfloor a+k\rfloor=\lfloor a\rfloor +k$. Therefore your substitution $\left\lfloor w-\lfloor x\rfloor\right\rfloor=\left\lfloor w\right\rfloor-\lfloor x\rfloor$ is correct.