Solve for range of $y$ in $x = \operatorname{round}(y + c)$

Question

Suppose I have

$$ x = \operatorname{round}(y + c) \\ $$

I want to solve for $y$, though it's not really possible in this case. Is it possible to get $y$ as a range of values based on some lower and upper bound where those bounds are dependent on $x,c$?

Answer 1

$5 = round(y + 3)$

Range is {y : $y \in R$, $1.5 \leq y < 2.5$}

For $x = round(y + c)$

Range is {y : $y \in R$, $\frac{x - c}{2} \leq y < (x - c + 0.5)$}, $x > c$