Why do they differ? Rules for addition/subtraction when simplifying equations

[bobisaka]

When simplified, in the first highlighted equation, the constant is subtracted from the variable. In the last highlighted equation the constant is added to the variable, should it not be -(-17 - 9) = 8?

Edit: I believe i read it wrong. In the example, in the checking step of the equations I believe they just put the variables number into the equation but its not simplified further just yet, which confused me.

 

[lev888]

Please post the steps you are asking about. I don't see where "the constant is subtracted from the variable". If you are talking about this:
-(y - 9) = 8 => -y+9=8
then we are distributing (-1): -(y-9) = (-1)*(y-9) = -y + 9.