document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72059>Question 72059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51520 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=51520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is as much an exercise in interpreting the wording of this problem as it is doing the<BR>\n" );
document.write( "math work to solve it. Let's start with the first part:<BR>\n" );
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document.write( "\"The sum of n and three subtracted from twelve times n\"<BR>\n" );
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document.write( "This is not clearly written. I could interpret this two ways.  The first way is that I <BR>\n" );
document.write( "could assume that n is first added to 3 and that result is subtracted from 12 times n.<BR>\n" );
document.write( "Written in algebraic form this would be 12*n - (n + 3)<BR>\n" );
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document.write( "But I could also interpret this as twelve times n is 12*n and three subtracted from that <BR>\n" );
document.write( "is (12*n - 3). Then add n to that to get n + 12*n - 3 which simplifies to 13*n - 3<BR>\n" );
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document.write( "I'm going to assume the first one is what they intended and they wanted you to use. But it<BR>\n" );
document.write( "would be much better if they had said \"from the product of 12 and n subtract the quantity<BR>\n" );
document.write( "resulting from the sum of n and 3. It is important that math equations be clearly stated<BR>\n" );
document.write( "to avoid misunderstandings.<BR>\n" );
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document.write( "12*n - (n + 3) <BR>\n" );
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document.write( "and this simplifies to 12*n - n - 3 which reduces to 11*n - 3<BR>\n" );
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document.write( "The next part of the problem says \"is the same as\" which really means \"is equal to\". So<BR>\n" );
document.write( "we now have 11*n - 3 = ????  Now we need to interpret what the problem says after the<BR>\n" );
document.write( "\"is the same as\" wording.<BR>\n" );
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document.write( "The next thing the problem says is \"negative eleven plus the product of 2 and the difference <BR>\n" );
document.write( "of n and five\". This is more clear than the statement describing the operations on the other<BR>\n" );
document.write( "side of the equation.  Let's start at the end and work backwards. The difference of n and 5 is<BR>\n" );
document.write( "written as (n - 5). The product of 2 and that term is 2*(n - 5).  Then we add negative 11<BR>\n" );
document.write( "to that and the whole expression is -11 + 2*(n - 5)<BR>\n" );
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document.write( "This now makes our equation:<BR>\n" );
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document.write( "11*n - 3 = - 11 + 2*(n - 5)<BR>\n" );
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document.write( "Multiply the 2 times the (n - 5). When you do you get 2*n - 10.  Substitute this into the<BR>\n" );
document.write( "equation and you get:<BR>\n" );
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document.write( "11*n - 3 = - 11 + 2*n - 10<BR>\n" );
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document.write( "On the right side combine the - 11 and -10 to get -21 and make the equation:<BR>\n" );
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document.write( "11*n - 3 = 2*n - 21<BR>\n" );
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document.write( "Get rid of the -3 on the left side by adding +3 to both sides. This addition results in:<BR>\n" );
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document.write( "11*n = 2*n - 18<BR>\n" );
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document.write( "Finally, eliminate the 2*n on the right side by subtracting 2*n from both sides to get:<BR>\n" );
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document.write( "9*n = -18<BR>\n" );
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document.write( "Now all you have to do is divide both sides by 9 to get n = -18/9 = -2. <BR>\n" );
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document.write( "Perhaps the most important lesson to be learned from this (in addition to the fact that<BR>\n" );
document.write( "it's easy to think you have said something clearly when you have not) is the importance<BR>\n" );
document.write( "of writing things so that there is little chance for misunderstanding.  Hope this helps<BR>\n" );
document.write( "you to understand the problem and enables you to argue with your teacher if he or she <BR>\n" );
document.write( "elected the other interpretation for the left side of the equation. [The other interpretation<BR>\n" );
document.write( "does not give a nice even answer like n = -2.]<BR>\n" );
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