SOLUTION: 14 = 2/3(9y - 15) Please show me how to solve the problem. I am a parent trying to help my child with her pre-Algebra. There is no example in her textbook (Prentice Hall Mat

Algebra ->  Inverses -> SOLUTION: 14 = 2/3(9y - 15) Please show me how to solve the problem. I am a parent trying to help my child with her pre-Algebra. There is no example in her textbook (Prentice Hall Mat      Log On


   

Question 182487: 14 = 2/3(9y - 15)
Please show me how to solve the problem. I am a parent trying to help my child with her pre-Algebra. There is no example in her textbook (Prentice Hall Mathematics Pre-Algebra) FLORIDA. It has been many years since I was in school and, frankly, I can't figure it out! I don't know which operation to perform first.
Thanks.
Lin Daily
Found 3 solutions by tvandenberg, solver91311, MathGuyJoe:
Answer by tvandenberg(45) About Me  (Show Source):
You can put this solution on YOUR website!
I would assume you mean:
14+=+%282%2F3%29%2A%289y-15%29
So I'll solve that...
We want to remove the 2%2F3 from the right side of the equation, so we want to multiply both sides by 3%2F2.
14%2A%283%2F2%29=9y-15
Now, perform that math, and add 15 to both sides to isolate the 9y.
21%2B15=36=9y
To solve for y, divide both sides by 9.

y=36%2F9=4

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Step 1. Multiply both sides of the equation by 3:





Step 2. Apply the distributive property ():



Step 3. Add 30 to both sides:





Step 4. Multiply both sides by





Which you should turn around so it reads right, just for neatness sake:



Check:











True statement, so answer checks.

John

Answer by MathGuyJoe(20) About Me  (Show Source):
You can put this solution on YOUR website!
Hi Lin,
When trying to solve an equation, you try to isolate the variable ('y' in this case) by itself. In this case it'll be a multi-step process.
14 = 2/3(9y - 15)


Given your equation, the first step will be to get rid of the parentheses by multiplying 2/3 by (9y - 15). To do this, you need to multiply each of the elements in the parentheses by 2/3:
14 = (2/3 * 9y) - (2/3 * 15)


This simplifies to:
14 = (6y) - (10)


No more fractions -- we like to see that. =) Next step is to isolate 6y by itself - to do this we'll add 10 to both sides of the equation:
14 (+ 10) = 6y - 10 (+ 10)


This simplifies to:
24 = 6y


Next we divide both sides by 6 (so we're left with just 'y'):
24 (/ 6) = 6y (/ 6)


This simplifies to:
4 = y (or y = 4)


So 4 is our answer. To double-check it, we can substitute '4' for 'y' back in our original equation:
14 = (2/3 * 9y) - (2/3 * 15)
14 = (2/3 * 9(4)) - (2/3 * 15)
14 = (2/3 * 36) - (2/3 * 15)
14 = (24) - (10)
14 = 14


Looks good! Hope this helps.