Max was solving the equation below and isn’t sure if his answer is correct. explain to max how he can check his answer and then him identify any errors he made. provide the correct solution in your

how can he check his answer?

show the correct solution:

HOW CAN HE CHECK HIS ANSWER:
  HE CAN CHECK HIS ANSWER BY PLUGGING IN HIS X VALUE, AFTER HE GETS THE CORRECT ANSWER. 
SHOW THE CORRECT ANSWER: 
 3(3x+6) = 4(7x-1)
 9x+18 = 28x-4
 18 = 19x-4
 22 = 19x
 22/19 = x

CHECK:
3(22/19+6)/8 = 7(22/19-1)/6
45/38 = 45/38 ( Is true)

hope this helps!!

Well, first of all, the bottom 2 lines are cut off of the bottom of Max's solution,
and his final answer doesn't even appear there.

Here . . . let me complete it for you:
Under the part printed on the page should be:

             19  =  19x

               x  =  1



Now that Max has an answer, he can check it by writing it into the
original equation wherever there's an 'x' there.

The original:                                (3x-6) / 8  =  (7x-1) / 6

With Max's answer written in:    (3·1 - 6) / 8  =  (7·1-1) / 6

Simplify the left side:                   (3 - 6) / 8  =  (7·1-1) / 6
                                                          -3/8  =  (7·1-1) / 6

Simplify the right side:                       -3/8  =  (7-1) / 6
                                                          -3/8  =   6 / 6
                                                          -3/8  =  1
This result is not a true statement,
so 'x' can't be ' 1 '.

We have to go back, look through Max's work, and find his mistake.
(Actually, Max won't learn anything that way ... MAX should be looking through
his work to find his mistake. But life is not always fair.)

The third line of Max's solution is      3 (3x + 6)  =  4 (7x - 1)

Then he goes on to clear the
parentheses, and the next line is:        9x + 18  =  28x - 1

That's where his mistake is.  The left side is correct,
but on the right side, Max distributed the '4' incorrectly.
Shame on Max. 
This line should be                              9x + 18  =  28x - 4 .