What is the solution to

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.

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.

OK.

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

Your solution is correct. You correctly simplified the equation and ended up with the statement "6=7," which is not true. This means that there is no solution for x that makes the equation true. Therefore, the correct answer is option 3) no solution. Well done!