# For 6x+9 = 6x + a, what is the value of a such that there's infinitely many solutions?

$9$
If a were any other answer, they wouldn't be equal anymore. If a were $9$ however, $x$ could be anything and both sides would be the same.
For example. If we put $9$ for $a$, and then $1$ for $x$, our equation would be $15 = 15$. This is a sort of circular equation because it is stating the obvious and not getting you anywhere, but it shows that whatever you put for $x$ one side will force you to getting the same answer on the other side.
Therefore, if $a = 9$, there would be infinitely many solutions.