document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844280>Question 844280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2 and the largest odd number less than 3x+5 can be written in the form ax+b. What is a + B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508657 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=508657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is an even integer.<BR>\n" );
document.write( "you are looking for the positive difference between the following:<BR>\n" );
document.write( "smallest odd number greater than 7x-2<BR>\n" );
document.write( "greatest odd number less than 3x+5\r<BR>\n" );
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document.write( "if x is an even number that is positive, then the positive difference will be the larger number minus the smaller number.\r<BR>\n" );
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document.write( "if x is even, then 7x-2 will always be even, so the smallest odd number greater than that will be 1 greater which will be 7x-1.\r<BR>\n" );
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document.write( "if x is even, then 3x+5 will always be odd, so the greatest number smaller than that will be 2 less which will be 3x+3.\r<BR>\n" );
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document.write( "the positive difference will be (7x-1) - (3x+3) which will be equal to 7x - 1 - 3x - 3 which will be equal to 4x - 4.\r<BR>\n" );
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document.write( "this is in the form of ax + b, where a is equal to 4 and b is equal to -4.\r<BR>\n" );
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document.write( "the equation is 4x-4.\r<BR>\n" );
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document.write( "the following table shows that this formula give you the positive difference each time.<BR>\n" );
document.write( "the fourth and fifth column should be the same and they are, confirming this is true.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "x	7x-1	3x+3	(7x-1)-(3x+3)	(4x-4)\r\n" );
document.write( "				\r\n" );
document.write( "2	  13	  9	       4	    4\r\n" );
document.write( "4	  27	  15	       12	    12\r\n" );
document.write( "6	  41	  21	       20	    20\r\n" );
document.write( "8	  55	  27	       28	    28\r\n" );
document.write( "10	  69	  33	       36	    36\r\n" );
document.write( "12	  83	  39	       44	    44\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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