Ex 2:

-2x+7=22
-2x+7-7=22-7
-2x=15
-2x/(-2)=15/(-2) I do not have to switch the equality sign. Even if I did it would not look any different.
x=-7.5
Check:
-2x+7=22
-2(-7.5)+7=22 my solution is that x=-7.5 so I will just put that in to see if it works.
15+7=22
22=22
Yes. It does work. I have solved it correctly for sure. And I can write my solution as {x|x=-7.5} but usually with equations we just leave the solution as x=-7.5 because x is just one value and not a whole set. But you can use this set notation here too if you like.