What is the solution to

Question

x+5+x+1+x=3(x+2)+1
1)x=0
2)x=3
3)no solution
4) infinite
I got #3 no solution
x+5+x+1+x=3(x+2)+1
x+5+x+1+x=3x+6+1
3x+6=3x+7
-3x -3x
6=7 so no solution
Is this correct?
Thanks for checking over my work.

Answer 1

correct

If your x's drop out and you end up with a false statement, such as our 6 = 7, then there is NO solution
if, however, the x's drop out and you end up with a true statement, there would have been an infinite number of solutions.

Answer 2

OK.
Thanks for the added information explaining how the answer could have been different.
Thank you for your help!