To check if x = 9 is the solution, we need to replace every x with 9 and simplify
(3+x)/4 = 3
(3+9)/4 = 3
12/4 = 3
3 = 3
We get the same thing on both sides, so the last equation is a true equation. This means that the first equation is a true equation when x = 9. Therefore, the solution x = 9 is confirmed.
