The page numbers of an open book totalled $871$. At what pages was the book open? So far I have $x + (x-1) = 871$. This has led to one page being $435$ and the other, $436$. Is there anything needing alteration, or is this equation workable?

This equation (the equation you wrote) works.
x+ (x−1) = 871.
However, the equation x + (x + 1) = 871 also works, since these two numbers are also consecutive numbers.
Edit: The solution to the second equation yields the exact same answer.
