Question regarding frations with variables?

May 2010
10
0
El Cajon, CA
Hello, I feel ridiculous asking this question but I just cannot remember.

This is my problem:

5/6x+1/2=5/3x

I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

Thank you!!
 

Pim

Dec 2008
91
39
The Netherlands
I feel that, rather than getting the common denominatior and cross-multiplying, this question is better solved by moving the x's to the RHS

5/6x + 1/2 = 5/3x
1/2 = 5/3x-5/6x
1/2 = 10/6x-5/6x
1/2 = 5/6x
x = 6/10 = 3/5
 
Last edited:
May 2010
10
0
El Cajon, CA
My teacher gave us the answer of x=5/3, is that wrong?
 
May 2010
53
1
Altlanta GA
ok, i think i have this, but not 100% sure.

step one: because it is a fraction, you owuld mult. both sides by 6x = 1.
then you would be left of with 5/1 + 1/2. which i hope you can do.

the other side is where i get confuesd. you have to cross mult, and if you did this, you would end up witha fraction again. is that what you are supost to get??
 

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
Hello, I feel ridiculous asking this question but I just cannot remember.

This is my problem:

5/6x+1/2=5/3x

I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

Thank you!!
It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

I am assuming you mean \(\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}\)

Multiply through by \(\displaystyle 6x\)

\(\displaystyle 5 + 3x = 10\)

Solve for \(\displaystyle x = \frac{5}{3}\)
 
May 2010
10
0
El Cajon, CA
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers (Worried)
 
Feb 2010
1,036
386
Dirty South
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers (Worried)

\(\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}\)

\(\displaystyle \frac{5}{6x} - \frac{5}{3x} = - \frac{1}{2} \)

\(\displaystyle \frac{5}{6x} - \frac{10}{6x} = \frac{-1}{2}\)

\(\displaystyle \frac{5-10}{6x} = \frac{-1}{2}\)

\(\displaystyle \frac{-5}{6x} = \frac{-1}{2}\)

cross multiplication gives:

\(\displaystyle 6x = 10\)

\(\displaystyle x = \frac{5}{3}\)

Clear??
 
May 2010
10
0
El Cajon, CA
It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

I am assuming you mean \(\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}\)

Multiply through by \(\displaystyle 6x\)

\(\displaystyle 5 + 3x = 10\)

Solve for \(\displaystyle x = \frac{5}{3}\)

Yes that is what I meant, sorry I wasn't sure how to actually make fractions on here.

Ok I'm understanding a little better, the only thing I'm confused about it the 5+3x=10?? How do you get 10?


Sorry I'm terrible at fractions and math in general.
 

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers (Worried)
You are given: \(\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}\)

Multiply each term by \(\displaystyle 6x\) as this is the lowest common denominator of \(\displaystyle 2, 3 \text{ and } 6x\) (Just like 24 is the lowest common denominator of 3,4 and 6)

Multiplying by the LCD will remove the fraction to give a simple linear equation

\(\displaystyle \frac{5}{6x} \cdot 6x + \frac{1}{2} \cdot 6x = \frac{5}{3x} \cdot 6x\)

When you do some cancelling you get \(\displaystyle 5+3x=10\). Can you find x from this last equation?
 
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