There's no reason behind why 2(x +3) = 3x + 3 (or, after distribution, 2x + 6 = 3x +3). This is because the equation is given. Unless it's a word problem, there's never reasoning behind the equation itself, but there's reasoning behind the answer.
However, X is not equal to 3 because, when you substitute 3 in for x on both sides, you get a not true statement. This statement is that the results are equal to each other, which is false. I'll show you how.
2(3+3) = 3(3) +3
2(6) = 3(3) + 3
12 = 9
As you can see, you get that 12 = 9, which, logically, is false. The true answer to the equation is
2(x +3) = 3x +3 (Step One: Distribute the two)
2x +6 = 3x +3 (Step Two: Combine like terms on one side of the equation. If there are none, you can begin combining like terms on other sides of the equation. For this equation, subtract 2x from both sides of the equation, and also subtract three (NOT 3x) from either side.)
3 = x
Wait... I just got the same answer... Hm, there's something wrong here! I think the equation itself is impossible! How strange!
