2x+16=7+2x
how do you solve if the variable is the same on both sides of the equation

First subtract the 7 from both sides and that would equal 2x+9=2x then subtract 2x and the answer is 9

There are no real solutions to this equation and that would be your answer.
If you subtract 7 from both sides you get 2x+9=2x. No value of x would make that equation true, so you have to write on your paper that there are no real solutions as your answer.