# Math Help - Solve the Equation

1. ## Solve the Equation

Another problem I just crossed. Going to be last for tonight, I need to rest.

$3r-3/r = 7/9$ Okay, he is what I've done.

Divided off the r and got $3-3=7/9$
I multiplied both sides of the equation by the reciprocal $9/7$
Now here's where I'm lost.

2. ## Re: Solve the Equation

Originally Posted by HellBunny
Another problem I just crossed. Going to be last for tonight, I need to rest.

$3r-3/r = 7/9$ Okay, he is what I've done.

Divided off the r and got $3-3=7/9$ ... huh?
I multiplied both sides of the equation by the reciprocal $9/7$
Now here's where I'm lost.
is the equation

$\frac{3r-3}{r} = \frac{7}{3}$

or

$3r - \frac{3}{r} = \frac{7}{9}$

?

3. ## Re: Solve the Equation

Originally Posted by skeeter
is the equation

$\frac{3r-3}{r} = \frac{7}{3}$

or

$3r - \frac{3}{r} = \frac{7}{9}$

?
The first one.

4. ## Re: Solve the Equation

Originally Posted by HellBunny
The first one.
\displaystyle \begin{align*} \frac{3r - 3}{r} &= \frac{7}{3} \\ 3(3r - 3) &= 7r \end{align*}

Now expand the brackets then collect like terms and solve.

5. ## Re: Solve the Equation

I don't have the slightest clue what happened. Why did you change the problem? I know it's still the same, just been rearranged.

6. ## Re: Solve the Equation

Originally Posted by HellBunny
I don't have the slightest clue what happened. Why did you change the problem? I know it's still the same, just been rearranged.
Maybe because you need to rearrange it so you can solve it...

I multiplied both sides by 3 to get rid of the fraction on the right, and multiplied both sides by r to get rid of the fraction on the left.

7. ## Re: Solve the Equation

I tried solving it and still hadn't came out with the right answer.
I use distributive property 3(3r-3)=7r ; 9r - 9 = 7r ; 9r = 7r + 9 ; I don't get what's next

8. ## Re: Solve the Equation

I made a typo in the previous equation ... the right side should be $\frac{7}{9}$ instead of $\frac{7}{3}$

$\frac{3r-3}{r} = \frac{7}{9}$

cross multiply ...

$9(3r-3) = 7r$

distribute on the left side ...

$27r - 27 = 7r$

add 27 and subtract 7r from both sides ...

$27r - 7r = 27$

combine like terms on the left side ...

$20r = 27$

divide both sides by 20 ...

$r = \frac{27}{20}$

you're done.

9. ## Re: Solve the Equation

I hate how I can look at a problem after its done and say to myself " I knew how to do that! " but couldn't figure out how to do it. Insane. Thanks you guys.