Math Help - Fractional Equation

1. Fractional Equation

(x-2)/2 - (x-8)/4 = 1/2

I think I am supposed to solve this as a proportion... but not sure
I would show my work, but I have tried this so many times it's not funny... I have gotten x=2, x=4, x=6, x=14, x=16... you get it... LOL
any help is greatly appreciated!!!

2. Re: Fractional Equation

Multiply everything by 4.

$\frac{4(x-2)}{2} - \frac{4(x-8)}{4}= \frac{4\times1}{2}$

3. Re: Fractional Equation

I ran out the equation like that and got x=4...
(x-2)/2 - (x-8)/4 = 1/2
(4x-8)/2 - (4x-8)/4 = 4/2
(2x-4) - (x-2) = 2
x-2 = 2
x = 4

I know I have to be doing something wrong, just not sure what it is... (btw, how do you get the fractions like that???)

4. Re: Fractional Equation

understand that the whole reason for multiplying each term by 4 is to clear the fractions ...

$\frac{4(x-2)}{2} - \frac{4(x-8)}{4} = \frac{4}{2}$

$2(x-2) - (x-8) = 2$

now finish it ...

5. Re: Fractional Equation

Originally Posted by Drummerman
(x-2)/2 - (x-8)/4 = 1/2

I think I am supposed to solve this as a proportion... but not sure
I would show my work, but I have tried this so many times it's not funny... I have gotten x=2, x=4, x=6, x=14, x=16... you get it... LOL
any help is greatly appreciated!!!
An alternative (better) method is to try to simplify the LHS before trying to solve anything. To do this, you would need to add the fractions, and to add fractions you need a common denominator. In this case, the lowest common denominator is 4.

\displaystyle \begin{align*} \frac{x - 2}{2} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{x - 2}{2} \cdot \frac{2}{2} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{2x - 4}{4} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{2x - 4 - (x - 8)}{4} &= \frac{1}{2} \\ \frac{x + 4}{4} &=\frac{1}{2} \end{align*}

This explains why multiplying by 4 is appropriate, it's because the simplification of the LHS gives 4 as the denominator, which then needs to be multiplied out.

6. Re: Fractional Equation

Yes, that is an alternative method- but I don't understand why you say it is better.

7. Re: Fractional Equation

Originally Posted by HallsofIvy
Yes, that is an alternative method- but I don't understand why you say it is better.
It is considered more elegant mathematically to simplify all equations before trying to solve them, as it makes the process of solving the equation much easier.

8. Re: Fractional Equation

thanks ProveIt!!! that helped so much!!!
I did this:
\displaystyle \begin{align*} 4*\frac{x+4}{4}&=4*\frac{1}{2}\\x+4&=2\\x&=(-2) \end{align*}
Thanks again for the help!!!