Casie
9th grade middle school/ secondary school student

My dad and I have been trying to figure, how to solve for x on any of these problems my teacher gives us. The problem is:

2h/3 + 1/2 = 5h/6 - 3/4

Thanks!!!!!!!!

Hi Casie

The first thing to realize is that an equation remains true if you multiply both sides of an equation by any number that you wish. If you look at the denominators of the fractions you will see 3, 2, 6, 4. Think of what a common denominator for these numbers could be. The simplest one is 12 since all the numbers are divisors of 12. So, instead of changing all the denominators to 12 you just need to multiply every term of both sides of the equation by 12. (Since the two sides of the equation are equal they will still be equal after you have 12 times as much on each side.)
  Your new equation is now 4x2h + 6 = 2x5h - 3x3 which becomes 8h + 6 = 10h - 9. You now want to get all the terms containing h on one side and all number terms on the other. Subtracting 8h from both sides gives 6 = 2h - 9. Now adding 9 to both sides gives 15 = 2h. Divide both sides by 2 and we now have the value of h that makes the equation true. Thus 15/2 = 2h/2 and so h = 15/2 = 7 1/2.

Cheers
Jack