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March 12th, 2013, 07:14 AM   #1
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Rearranging equations - is this quite correct?

Hi guys just wondered if my working is quite correct?
I needed to rearrange the equation 4t = 3k/7t -5k and make k the subject. Here's what I did;

4t = 3k/7t -5k <---------multiply both sides by 7t
= 28t^2 = 3k - 5k <-------------add 5k to both sides
= 28t^2 +5k = 3k <------------swap sides
= 3k = 28t^2 +5k <----------divide both sides by three
= 3k/3 = 28t^2 +5k/3

and I end up with k = 28t^2 +5k/3

Any good?
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March 12th, 2013, 07:49 AM   #2
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Re: Rearranging equations - is this quite correct?

Check the first step. Are you sure you multiplied all member by 7t?

Later, in one side there is 3k, in the other side there is 5k. Why don't you subtract 3k from both side?
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March 12th, 2013, 07:59 AM   #3
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Re: Rearranging equations - is this quite correct?

Should I have multiplied the -5k by 7t also? That does not make sense? If I subtract 3k from both sides then I end up with k still on the wrong side of the equation?
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March 12th, 2013, 08:10 AM   #4
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Re: Rearranging equations - is this quite correct?

If the original equation is
4t = (3k - 5k)/7t
28tē = -2k
k = -14tē.

If the original equation is
4t = 3k/7t - 5k
28tē = 3k - 35kt
28tē = k(3 - 35t)
k = 28tē/(3 - 35t)
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March 12th, 2013, 08:40 AM   #5
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Re: Rearranging equations - is this quite correct?

                                           3k
The original equation is 4t = ---- -5k
                                           7t

So 4t equals 3k over 7t times k-6 if that makes it any more clear?

I decided not to swap sides straight away, though I think I could have, My aim was to get rid of the fraction first, so I multiplied 4t by 7t on the left, to get 28t^2 then the fraction on the right by 7t to cancel it. I did not multiply -5k by 7t, I did not think I had to. I was then left with 28^t2 = 3k-5k. So I then thought I should add 5k to both sides to undo the -5k, then I swapped sides and was left with 3k = 28t^2 +5k. Divided both sides by three and was left with three on its own.

It made sense to me? Did I mess up somehow? Should I have multiplied the term -5k by 7t also?
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March 12th, 2013, 08:51 AM   #6
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Your equation doesn't contain k-6 (or any 6).

You do need to multiply -5k by 7t.

After going wrong, you said you divided both sides by three and were left with three on its own. That doesn't make sense, as you ended up with k = 28t^2 +5k/3 and at no stage had three on its own.
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March 12th, 2013, 09:48 AM   #7
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Re: Rearranging equations - is this quite correct?

Alex, argue all you want, BUT:
if a = b/c - d
then a + d = b/c
so ac + cd = b
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