When you have this type of problem, you need to combine the like-terms and isolate the variable.
3x + 122 = 22x - 11
Add 11 to both sides to get rid of it
3x + 122 + 11 = 22x - 11 + 11 (-11 + 11=0)
3x + 133 = 22x
Then you would bring the 3x to the other side, so subtract 3x from both sides
3x + 133 = 22x
-3x -3x
133 = 22x - 3x
133 = 19x
Then divide both sides by 19 to isolate x
133/19 = 19x/19
133/19 = 7, so x = 7
Hope this helps!!