If anyone knows how to set this up and explain to me I would be so grateful.

[SIZE="2"]2/3(y-3) = 1/3y[/SIZE]

I know to remove the parenthesis, I multiply 2/3 x 3 (which is 2)

so: 2/3y - 2 = 1/3y

Now I know I must combine the y's and change the sign to positive AND THAT IS WHERE I GET STUCK

isn't it: 3/2(2/3)y = 3/2(1/3)y + 2???

then: y=1/2+2

then: y=2 1/2

But the answer in my book is 6
Please help me find what I am doing wrong.

Thanks so much

rudi_in

Hello and thank you for posting your question to the Ask Me Help Desk!

You are correct in distributing the 2/3 to the items in parentheses.

You are also correct in stating that the y variable components must be combined.

You can do this in an easy way by subtracting 1/3y from both sides instead of multiplying by 2/3
As long as we are fair and do the same thing to both sides we can keep everything equal.

2/3y - 2 = 1/3y
-1/3y = -1/3y

1/3y - 2 = 0

Now we can add 2 to both sides...

1/3y - 2 = 0
+ 2 = +2

1/3y = 2

Now you can divide both sides by 1/3.

1/3y ÷ 1/3 = 2 ÷ 1/3

This gives us...

y = 6

fredg

Hi,
As a past 13 years High School Math teacher, teaching Algebra, among other courses, I do hope you will look at your math book.
The answer before mine is very good.
There are different ways of solving equations. The math book you have explains, with examples, of how to do it.
If you still don't understand, please ask your teacher for help. I am sure there are others who don't understand either!
Best of luck.