Simple Rearranging Formlua

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nortski

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Feb 27, 2020
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I am struggling to understand why my answer is different from the actual answer to this simple formula rearrangement:

Make x the subject:

Q) v = (2/3)x - 2
Actual answer) x = (3v + 6) / 2
My answer) x = (3v + 2) / 2

My revision guide states to get rid of the fraction before anything else and then rearrange. So my working is:
step 1) 3v = 2x - 2
step 2) move the -2 to the other side = 3v + 2 = 2x
step 3) divide by 2 = (3v + 2) / 2 = x

To get the actual answer it's apparent that the 2 was moved to the opposite side first.
Can someone please clarify this for me. Thanks.
 
nortski said:
I am struggling to understand why my answer is different from the actual answer to this simple formula rearrangement:

Make x the subject:

Q) v = (2/3)x - 2
Actual answer) x = (3v + 6) / 2
My answer) x = (3v + 2) / 2

My revision guide states to get rid of the fraction before anything else and then rearrange. So my working is:
step 1) 3v = 2x - 2
step 2) move the -2 to the other side = 3v + 2 = 2x
step 3) divide by 2 = (3v + 2) / 2 = x

To get the actual answer it's apparent that the 2 was moved to the opposite side first.
Can someone please clarify this for me. Thanks.
Click to expand...
Step 1 is Incorrect. Could you explain how you got your result?
 
lev888 said:
Step 1 is Incorrect. Could you explain how you got your result?
Click to expand...
Hi.
I thought you had to multiply all terms by the denominator: 3 . v = (3 . 2 / 3)x - 3 . 2
The 3's then cancel each other out leaving: 3v = 2x - 2

This is probably where I'm going wrong.
 
nortski said:
Hi.
I thought you had to multiply all terms by the denominator: 3 . v = (3 . 2 / 3)x - 3 . 2
The 3's then cancel each other out leaving: 3v = 2x - 2

This is probably where I'm going wrong.
Click to expand...
What happened to the last term: 3*2?
 
nortski said:
Hi.
I thought you had to multiply all terms by the denominator: 3 . v = (3 . 2 / 3)x - 3 . 2
The 3's then cancel each other out leaving: 3v = 2x - 2

This is probably where I'm going wrong.
Click to expand...
That should compute to 6 - giving you:

3v = 2x - 6

And ... finish it...
 
I will not push that you should move the -2 to the other side first, but will point out that if you had, then you would not have made your mistake.
 
What do you get if multiply 63/5 - 5 by 5?

63/5 - 25/5 = 38/5. Now when we multiply 63/5 - 5 by 5, ie multiply 38/5 by 5 we get 38.

Using your method you get 63-1 (1 because you divide the 5 by 5) = 62.

Which is correct?
 
Just quickly, so if the -2 was over the same denominator of the +2, then would both cancel?
 
nortski said:
Just quickly, so if the -2 was over the same denominator of the +2, then would both cancel?
Click to expand...
Cancel to what?

1st of all the phrase cancels out is not clear. After all, 7-7 cancels out to 0, while 7/7 cancels out to 1. And 14/7 cancels out to 2.

Again, your question is not clear. +2/2 would cancel out to 1 while -2/2 would cancel out to -1.

It probably is best never to say cancels out, but if you do then you MUST say cancels out to some number.
 
Jomo said:
Cancel to what?

1st of all the phrase cancels out is not clear. After all, 7-7 cancels out to 0, while 7/7 cancels out to 1. And 14/7 cancels out to 2.

Again, your question is not clear. +2/2 would cancel out to 1 while -2/2 would cancel out to -1.

It probably is best never to say cancels out, but if you do then you MUST say cancels out to some number.
Click to expand...
What I should have said is what if two terms were over the same denominator:
(2-4) / 3
Then to get rid of that fraction: (3.2 - 3.4) / 3 is the same as 2 - 3 right?
 
nortski said:
What I should have said is what if two terms were over the same denominator:
(2-4) / 3
Then to get rid of that fraction: (3.2 - 3.4) / 3 is the same as 2 - 3 right?
Click to expand...
If you had \(\displaystyle \dfrac{2-4}{3}\) and wanted to multiply by 3.

You can say \(\displaystyle 3(\dfrac{2-4}{3})=2-4\), NOT 2-3 because the 3 cancel out to 1
 
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