I can spend ages on it and get it right and then be like we'll I did it but I have no idea how. And then ones that are easier I will get wrong because I do too much to them. This question I know how to get the answer to the solution but I do not know why the examples approach is wrong as he did what I would do to check... Nor do I understand what the student should of done instead to check.
Any help and feedback is appreciated and by this time next week I hope I will love algebra haha
Also I am not good with computers so hope I uploaded the pics correctly
You did fine with the pictures.
I assume you solved the problem correctly yourself; there are several correct ways to do it.
I suppose you also see the student's error in "multiplying by 6" in different senses on the two sides.
As for the check, the only thing I see wrong is formal: It is technically incorrect to start with an equation you don't yet know to be true. I would either not write "= 12" on each line (merely ending with the fact that the left-hand side is 72, which is not equal to 12 as required by the problem), or write the = sign with a question mark to say, "This is not a known fact, but a question: is it true?" Then at the end we can say that it is not.
Maybe you have been taught something like that, and are expected to say it. If not, the question seems a little picky. Or maybe I've missed a bigger issue.
A problem like this is intended to teach you to look carefully at your work and recognize subtle errors; it took me a while to see the error in the student's solution, because it's easy to believe what someone tells you (even if it's your own past self!). How you write the check is not nearly as important as doing it; but it's also important to understand what you are doing, checking whether the equation is true after putting in your solution.
