No, he wasn't being sarcastic- you write very well and clearly. However, I am concerned about the kind of problems you keep posting. You post some very difficult problems and some that depend only on basic ideas of algebra, the kind that are typically taught at age 10 or 11. Further, you seldom show any attempt to solve the problems youself. Given the kind of problems you have posted before, I find it very difficult to believe that you have absolutely no idea how to solve \(\displaystyle w- 9\frac{1}{2}= 16\).
The very first thing you should have learned about solving equations is that "solve an equation" means to have the unknow, here, w, alone: w= some number.
And soon after that, you should have learned that you have to do the same thing to both sides. Now, what arithmetic operation do you have to do to change "\(\displaystyle w- 9\frac{1}{2}\) to just w?
(If it's bothering you at all, \(\displaystyle 9\frac{1}{2}= 9+ \frac{1}{2}= \frac{18}{2}+ \frac{1}{2}= \frac{19}{2}\).)