Quote Originally Posted by qwertysaur View Post
Incorrect. If you substitute x = 0 then you will get -7 = 19 which is wrong. The correct answer is no solution.
Proof
<pre>
x-7 = 19 + x
-x -x</pre>
-7 = 19, a contradiction indicating no solution.
You can see the fallacy in your work because ito get x=0 you had to multiply everything by x. However assume x is 0 you are simply multiplying everything by zero and all information is lost.
This, you can see it without doing any work.

Quote Originally Posted by Peegee View Post
but I added and mutiplied everything on both sides. Ergo it is valid. x = 0
It's only valid if you plug it back in and get a valid result.