document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191689>Question 191689</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780618503087/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is thirty-three.  Using x to represent the larger of the two numbers, translate \"the difference between six more than twice the larger number and the sum of the small number and three\" into a variable expression. Then simplify. \r<BR>\n" );
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document.write( "(6 + 2x) - (x + 3) = 33  ?  It just doesn't look right?   I am having a HARD time on these kind of problems.   <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143804 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The reason that it doesn't \"look right\" is because it isn't.  However, you started out on the right track.\r<BR>\n" );
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document.write( "Take it in logical pieces:\r<BR>\n" );
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document.write( "Let <i><b>x</b></i> represent the larger of the numbers, just like the instructions say.\r<BR>\n" );
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document.write( "You got the first bit of it right when you translated: \"six more than twice the larger number\" into <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 6 + 2x\">\r<BR>\n" );
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document.write( "But then you tried to represent \"the sum of the small number and three\" as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x + 3\">, when in fact that expression represents the sum of the <i><b>large</b></i> number and three.\r<BR>\n" );
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document.write( "The key here is the first statement in the problem. \"The sum of two numbers is thirty-three.\"   If one of the numbers is <i><b>x</b></i>, then the other one has to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 33 - x\">.  (Let one number be <i><b>x</b></i> and the other <i><b>y</b></i>.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x + y = 33 \ \ \Rightarrow\ \ y = 33 - x\">)\r<BR>\n" );
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document.write( "Now you can say the sum of the small number (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 33 - x\">) and three is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 33 - x + 3 = 36 - x\">\r<BR>\n" );
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document.write( "The second thing you did incorrectly was try to make this into an equation.  The problem didn't ask for an equation, and it couldn't.  The problem didn't give you anything to which the expression might equate.  So, just an expression -- no equals sign.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (6 + 2x) - (36 - x)\">\r<BR>\n" );
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document.write( "Finally, you need to collect like terms to simplify the expression.  Don't forget to use the distributive property across the second set of parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6 + 2x - 36 + x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x - 30\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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