Like Terms in Algebra

The problem is, you tried to solve

-9n - 7 + 1

like this

-9n - (7 + 1) = -9n - 8

But because of order of operations, it should be done like this:

-9n (-7 +1) = -9n - 6 

The subtraction sign must be considered as a negative when doing algebra like this, because

-9n - 7 + 1 (the original problem)

is the same thing as 

-9n + (-7 +1)

which equals -9n + (-6)

which equals -9n - 6

Hope that helps! Let me know if it didn't and I'll explain it in another way. :)