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Question 7935: Here is my equation : A(M+N)=BN-4m
This is what I have so far: -BN+AN=-AM-4M
Is this right? If so what's next?
Answer by AnlytcPhil(1807)   (Show Source):
You can put this solution on YOUR website! >>Here is my equation : A(M+N)=BN-4M
This is what I have so far: -BN+AN=-AM-4M
Is this right? If so what's next?<<
`
We have to know whether you are solving for A, M, or N.
You forgot to tell us which of the three letters you are
supposed to solve for. It looks as though you are
solving for N since you got all the terms with N on the
left side, so I'll assume you are solving for N
`
A(M+N) = BN-4M
`
`AM+AN = BN-4M
`
-BN+AN = -AM-4M (this is what you have so far)
`
Next step is to factor out N on the left side:
`
N(-B+A) = -AM-4M
`
Now we divide both sides by the parenthetical expression
(-B+A)
`
N(-B+A) ` `-AM-4M
-------- = -------
`(-B+A)` ` `(-B+A)
`
Now we can cancel the (-B+A)'s on the left
`
N(-B+A) ` `-AM-4M
-------- = -------
`(-B+A) ` ` (-B+A)
`
` ` -AM-4M
N = -------
` ` `(-B+A)
`
This will do for an answer. However we like to see if
we can make the answer look simpler. Factor -M out of
the numerator
`
` ` -M(A+4)
N = -------
` ` `(-B+A)
`
We can dispense with the parentheses in the denominator:
`
` ` -M(A+4)
N = -------
` ` ` -B+A
`
Next factor -1 out of the denominator
`
To understand how to do this, place 1's in front of the
letters in the denominator
`
` ` `-M(A+4)
N = ---------
` ` `-1B+1A
`
Now it's easy to see how to factor -1 out of the
denominator:
`
` ` -M(A+4)
N = -------
` ` -1(B-A)
`
We can now cancel the negative signs
`
` ` `M(A+4)
N = -------
` ` `1(B-A)
`
We don't need the 1 or the parentheses around the B-A
`
` ` `M(A+4)
N = -------
` ` ` B-A
`
This could be the simplest form, or you could remove
the parentheses in the numerator and have
`
` ` `MA+4M
N = -------
` ` ` B-A
`
One of these last two forms should be identical to
the answer given in your book.
`
Edwin
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