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Old Sep 2nd 2014, 10:05 AM   #1
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Help with a simple Linear Equation

Hi all, I'm struggling to get the answer from an exercise I'm doing. I've tried multiple things and still I'm not getting the answer I should be! Anyways, here it is...

2/3(1/2-x+1/4)=5/6

Apparently the answer is -4 but I cant seem to get it! (if someone can just write it out ill be able to see what you've done)

Much appreciation! Luke
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Old Sep 2nd 2014, 10:32 AM   #2
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Let's just replace the contents of the bracket with a variable, like this:

2/3( y )=5/6

y = 5/6 divided by 2/3 = 5/6 x 3/2 = 15/12 = 5/4

So 1/2-x+1/4 = 5/4

Take a quarter off both sides

1/2-x = 4/4 = 1

So x = -

Duh!

Somebody check my arithmetic.
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Old Sep 2nd 2014, 10:56 AM   #3
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I get the same answer as FarSight,
Either there is something missing, or the answer is not -4.

Perhaps if you were to offer a few more background details about the exercise it might point to where our misapprehension arises.
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Old Sep 2nd 2014, 11:24 AM   #4
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http://www.scribd.com/doc/113743471/...-word-problems

Here is the link to the problems, its number 51 and the answers are bellow. Thanks for getting back to me. On quite a few I've been getting the right answers, then on others they're completely wrong :S
Basically I've been getting rid of the fractions then treating it as a simple linear equation. This was throwing me off with fractions being inside the parantheses as well as the outside. I assumed there was a different method with the answers I was pulling out!

Last edited by Luke101; Sep 2nd 2014 at 11:48 AM.
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Old Sep 2nd 2014, 12:15 PM   #5
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Parentheses are very important things! In your post you wrote:

2/3(1/2-x+1/4)=5/6

which is:



The solution to this is indeed x = -1/2. But problem #51 is actually this:



which is entirely different. In your post you should have written it as:

2/3(1/2-(x+1)/4)=5/6

Note the extra set of parentheses! To solve this:

1. Multiply both sides by 3/2 to get: 1/2-(x+1)/4=5/6 x 3/2 = 5/4
2. Subtract 1/2 from both sides: -(x+1)/4 = 5/4 - 1/2 = 3/4.
3. Multiply both sides by 4: -(x+1) = 3/4 x 4 = 3
4. Multiply both sides by -1: x+1 = -3
5. Subtract 1 from both sides: x = -3-1 = -4.

Last edited by ChipB; Sep 2nd 2014 at 12:23 PM.
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Old Sep 2nd 2014, 12:46 PM   #6
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Sorry for the mistake and thank you for the reply! I was attempting it by using the LCM to get rid of the fractions, I must have tried like 20 times haha, I'm guessing you can't use that method on this problem?

Thanks again, Luke
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Old Sep 2nd 2014, 12:51 PM   #7
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Finding the least common multiple, or least common denominator, is useful when adding or subtracting fractions. It really has nothing to do with this problem (other than the one step where you subtract 1/2 from 5/4).
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Old Sep 3rd 2014, 02:15 PM   #8
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..

Thank you again, that was very helpful. I've been able to work through to the final problem, however the parentheses within those brackets are throwing me off a little...
Firstly the middle set has a minus before it, if memory serves correct I watched a video that mentioned that you just switch what is within to the opposite... Not sure if this is correct? Also because the equation is 36[...(...)...] does that mean I multiply EVERYTHING within by '36'?
(If you are wondering where 36 came from thats what I came up with by converting all the fractions to the same LCD (24) to getting rid of the fractions)

Kind regards, Luke
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Old Sep 3rd 2014, 03:34 PM   #9
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-(x+1)/6 is the same as (-x-1)6, if that's what you mean. And yes - the 36 multiplies all the terms within the brackets.
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