Fractional Coefficients

Date: 1/21/96 at 21:24:28
From: Anonymous
Subject: Fractional Coefficients

I am completely stuck. Help! My teacher said it was wrong.

x-4/8 - 5-2x/3 = 7/12

This is what I got:
3x - 12 - 40 + 16x = 14
19x - 52 = 14
19x - 52 + 52 = 14 + 52
19x / 19 = 66 / 19
x = 3.473

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Date: 5/30/96 at 12:16:41
From: Doctor Alain
Subject: Re: Fractional Coefficients

Well, if we put x=3.473 in the first equation (x-4/8-5-2x/3=7/12)
we get

-4.342 = 7/12

So yes, there is an error. If after reading your solution, you can't
see where the error is, here is how you can find it. 

Try x=3.473 in the third line you wrote:

19 (3.473) -52 +52 = 14 + 52
65.987 = 66

This is about right (the difference is due to roundoff error) so
there is no error past the third line you wrote. Therefore the error 
must be in your first second or third line. 

Let's try x=3.473 in the second line you wrote

19 (3.473)-52 = 14
13.987 = 14.

It still looks good, so there isn't any error past your second line. The
error must be in the first or second line. 

Let's try x=3.473 in the first line you wrote.

3 (3.473) - 12 - 40 + 16(3.473) = 14
13.987 = 14

So there is no mistake past your first line. There is an error
but it isn't past your first line. It must be on the first line.

So now you know where to look. The mistake is on the very first
line. Look at it again. I'm sure you will see your error.

x-4/8 - 5-2x/3 = 7/12

A good way to start the problem would be to multiply both
sides by 12.

12x - 6 - 60 - 8x = 7

I'm sure that you can complete the rest of the solution.

-Doctor Alain,  The Math Forum