Solve for x: 4 over 5 x + 4 over 3 = 2x

Question

anonymous · Answer

Fraction within a fraction?

anonymous · Answer

Or multiplying two fractions?

anonymous · Answer

Maybe this will help. 4/5 X + 4/3 =2X

anonymous · Answer

Is this correct?

anonymous · Answer

Ah, so it's (4/5)(X) + (4/3) = 2X

anonymous · Answer

Yes

anonymous · Answer

Well fractions are messy, so the first thing to do here would be to change the equation so that it no longer has fractions.

anonymous · Answer

Do you know how to do that?

anonymous · Answer

No. Fractions is my weakness in algebra

anonymous · Answer

:) Mine too, you should ask my math teacher.  Anyway, a common denominator is needed.
Your denominators right now are 5, 3 and 1.

anonymous · Answer

You can always multiply by 1, and 1 can be anything over itself.  
You can also multiply individual terms by various versions of "1."

Knowing this and that you need a common denominator, what will you do next?

anonymous · Answer

No. But I do know is that I have to do something to find a common denominator so I can get rid of the fractions.

anonymous · Answer

I just don't know how to do that step yet.

anonymous · Answer

Mhm, that something you have to do is multiply by one. :)

I'll do one for you if you can tell me what that common denominator can be!
HINT: The common denominator is a number that is divisible by all of the denimonators.

For example, (1/2) and (1/4) can both be something over 4.

anonymous · Answer

denominators*

anonymous · Answer

20 is divisible by the denominators 4 and 5

anonymous · Answer

Sure, 20 will work.  It isn't the lowest common denominator, but it should work.

anonymous · Answer

Okay

anonymous · Answer

Now how will you change (4X/5) to something over 20?

anonymous · Answer

Would I multiply?

anonymous · Answer

Yes!  By a version of one.  Let me do one for you as an example:

anonymous · Answer

Okay

anonymous · Answer

attachment

anonymous · Answer

Oh!!

anonymous · Answer

:D Yay!  Had an epiphany?

anonymous · Answer

Haha Yes

anonymous · Answer

Can you solve it?  :)

anonymous · Answer

Let me check.

anonymous · Answer

Would it be 4/5?

anonymous · Answer

Hold on, aren't one of your denominators 3?

anonymous · Answer

I don't believe 20 is a common denominator if that's true.  LOL.

anonymous · Answer

20 is not nicely divisible by 3.  You'd only create another fraction.  Unless the question was written wrong.

anonymous · Answer

Would the common denominator be 15?

anonymous · Answer

Yes, if the denominators are 5, 3 and 1, the lowest common denominator would be 15.  Sorry I didn't catch that sooner.

anonymous · Answer

It's fine

anonymous · Answer

So what would the answer be now that the number changed?

anonymous · Answer

What did you get?  I can tell you whether it's right or wrong.

anonymous · Answer

Sorry Im confused. I forgot what to do when I found the common denominator. I know its 15 but i dont know what to do after that.

anonymous · Answer

Get all of them to be over 15.  Once that's done, the denominators become negligible.  I can show you how that works algebraically.

anonymous · Answer

Ok that would be good.

anonymous · Answer

Do you know the equation now with the common denominator?  Tell me what it is if you do.

anonymous · Answer

Would it be 4/15 X + 4/15 =2X

anonymous · Answer

The 2X also needs to be over the same denominator!  Only then can we remove the fractions.

anonymous · Answer

4/15 X + 4/15 = 2X/15

anonymous · Answer

Doesn't quite work that way.  Remember I did one for you?  Look at the image again.

anonymous · Answer

To get that denominator, you have to multiply 4X/5 by 3/3, which is "1."

4X/5 times 3/3.  Do you know how to multiply fractions?

anonymous · Answer

Cross multiply?

anonymous · Answer

That's one way to do it, but another is to simply multiply across.

anonymous · Answer

attachment

anonymous · Answer

Yeah but now there is a 3 as a denominator

anonymous · Answer

Yes, and you have to repeat the same process to make that 3 a 15.

anonymous · Answer

And the 1 that's hiding under the 2X a 15, too.

anonymous · Answer

I still dont understand what to do.

anonymous · Answer

Would it be 4/15 X + 4/15 = 2X/15

anonymous · Answer

No.

anonymous · Answer

attachment

anonymous · Answer

Actually, since you're multiplying both sides by 1/15 it's fine to do that as well, but that won't always work.

anonymous · Answer

Ah, you aren't though.

anonymous · Answer

So actually it's completely wrong.  You're introducing denominators out of the blue.

anonymous · Answer

But anyway, I hope that helps.  I should do my own work now.

anonymous · Answer

Do you have the answer?

anonymous · Answer

You should be able to come up with it yourself.

anonymous · Answer

Re-read.

anonymous · Answer

I just dont know what to do.

anonymous · Answer

I've given you your first step, you should be able to take it from there.  Are you opening the images I've sent?  Try checking those again.  Good luck.