First of all, you made a little mistake when you subtracted 14/24 from both sides. You would have 24/24 - 14/24 = 10/24 on the right side of the equation. Then, you would have:

-64/24x = 10/24

Next, divide both sides by -64/24 in order to get "x" by itself. You will have x = - 5/32, which is your answer.

BUT . . .

But you got too complicated with your equation. Although you can figure it the way you did because what you did to one side of the equation you did to the other, you want to do the problem as simply as possible. First, make sure all your terms are added together on one side of the equation if they can be. In this case, add 7/12 to -5/8. You will only need to convert these to common denominators instead of converting all your terms to common denominators. 7/12 converts to 14/24 and -5/8 becomes -15/24.

14/24 - 15/24 = -1/24. So now you have:

-8/3x - 1/24 = 3/8 (Both sides are simplified).

Then, add +1/24 to both sides. You will have to find a common denominator again. 3/8 becomes 9/24. So, 1/24 + 9/24 = 10/24. The equation is now:

-8/3x = 10/24

Divide both sides by -8/3 to isolate "x". You have x = -5/32, Answ.



You see, we did not have to convert all the terms to a common denominator because all the terms still are in the same proportion. In other words:

Say you have 1/2 + 1/4. You need to add them together. You can make 1/2 become 2/4.

1/4 + 2/4 = 3/4

Now, you could have also coverted 1/2 to 10/20, but it still was 1/2. Remember anything multiplied by 1 is itself? That is exactly what you did---multiplied 1/2 by 1 to get a common denominator, although it was a fraction like 2/2.

1/2 x 2/2 (which is really another way of saying 1) = 2/4 (which is another way of saying 1/2).


Does this make sense? You might have to review a book like Cliff's QuickReview for Algebra. I used that book for preparing for the ACT and liked it a lot.