SOLUTION: The sum of n and three subtracted from twelve times n is the same as negative eleven plus the product of 2 and the difference of n and five.

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Question 72059: The sum of n and three subtracted from twelve times n is the same as negative eleven plus the product of 2 and the difference of n and five.
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of n and three subtracted from twelve times n is the same as negative eleven plus the product of 2 and the difference of n and five.
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EQUATION:
12n-(n+3)=-11+2(n-5)
12n-n-3 = -11+2n-10
11n-3 = 2n-21
9n = -18
n=-2
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Cheers,
Stan H.

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
This is as much an exercise in interpreting the wording of this problem as it is doing the
math work to solve it. Let's start with the first part:
.
"The sum of n and three subtracted from twelve times n"
.
This is not clearly written. I could interpret this two ways. The first way is that I
could assume that n is first added to 3 and that result is subtracted from 12 times n.
Written in algebraic form this would be 12*n - (n + 3)
.
But I could also interpret this as twelve times n is 12*n and three subtracted from that
is (12*n - 3). Then add n to that to get n + 12*n - 3 which simplifies to 13*n - 3
.
I'm going to assume the first one is what they intended and they wanted you to use. But it
would be much better if they had said "from the product of 12 and n subtract the quantity
resulting from the sum of n and 3. It is important that math equations be clearly stated
to avoid misunderstandings.
.
12*n - (n + 3)
.
and this simplifies to 12*n - n - 3 which reduces to 11*n - 3
.
The next part of the problem says "is the same as" which really means "is equal to". So
we now have 11*n - 3 = ???? Now we need to interpret what the problem says after the
"is the same as" wording.
.
The next thing the problem says is "negative eleven plus the product of 2 and the difference
of n and five". This is more clear than the statement describing the operations on the other
side of the equation. Let's start at the end and work backwards. The difference of n and 5 is
written as (n - 5). The product of 2 and that term is 2*(n - 5). Then we add negative 11
to that and the whole expression is -11 + 2*(n - 5)
.
This now makes our equation:
.
11*n - 3 = - 11 + 2*(n - 5)
.
Multiply the 2 times the (n - 5). When you do you get 2*n - 10. Substitute this into the
equation and you get:
.
11*n - 3 = - 11 + 2*n - 10
.
On the right side combine the - 11 and -10 to get -21 and make the equation:
.
11*n - 3 = 2*n - 21
.
Get rid of the -3 on the left side by adding +3 to both sides. This addition results in:
.
11*n = 2*n - 18
.
Finally, eliminate the 2*n on the right side by subtracting 2*n from both sides to get:
.
9*n = -18
.
Now all you have to do is divide both sides by 9 to get n = -18/9 = -2.
.
Perhaps the most important lesson to be learned from this (in addition to the fact that
it's easy to think you have said something clearly when you have not) is the importance
of writing things so that there is little chance for misunderstanding. Hope this helps
you to understand the problem and enables you to argue with your teacher if he or she
elected the other interpretation for the left side of the equation. [The other interpretation
does not give a nice even answer like n = -2.]