document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187236>Question 187236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find what x is so that 3x-1, 5x-4 and 2x+8 are consecutive terms of an arithmetic sequence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140347 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=140347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An arithmetic sequence is of the form: a, a+d, a+2d, a+3d, ..., a+nd\r<BR>\n" );
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document.write( "Note: I'm just adding a constant number to 'a' each time.\r<BR>\n" );
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document.write( "So if you subtract the 1st term from the second, you get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bd%29-a=a-a%2Bd=d ALIGN=MIDDLE  ALT=\"%28a%2Bd%29-a=a-a%2Bd=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you subtract the 2nd term from the 3rd term, you get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B2d%29-%28a%2Bd%29=%28a-a%29%2B%282d-d%29=d ALIGN=MIDDLE  ALT=\"%28a%2B2d%29-%28a%2Bd%29=%28a-a%29%2B%282d-d%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you subtract the 3rd term from the 4th term, you get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3d%29-%28a%2B2d%29=%28a-a%29%2B%283d-2d%29=d ALIGN=MIDDLE  ALT=\"%28a%2B3d%29-%28a%2B2d%29=%28a-a%29%2B%283d-2d%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So if you subtract ANY term from the next term, you will ALWAYS get the result of \"d\"\r<BR>\n" );
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document.write( "In other words, each term is separated by the same distance. \r<BR>\n" );
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document.write( "In our case, the first term is 3x-1, the second term is 5x-4 and the third term is 2x+8\r<BR>\n" );
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document.write( "So according to the logic above, this should be true (if the sequence is an arithmetic one):\r<BR>\n" );
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document.write( "2nd term - 1st term = 3rd term - 2nd term\r<BR>\n" );
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document.write( "which looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-4%29-%283x-1%29=%282x%2B8%29-%285x-4%29 ALIGN=MIDDLE  ALT=\"%285x-4%29-%283x-1%29=%282x%2B8%29-%285x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-4%29-%283x-1%29=%282x%2B8%29-%285x-4%29 ALIGN=MIDDLE  ALT=\"%285x-4%29-%283x-1%29=%282x%2B8%29-%285x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-4-3x%2B1=2x%2B8-5x%2B4 ALIGN=MIDDLE  ALT=\"5x-4-3x%2B1=2x%2B8-5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=2x%2B8-5x%2B4 ALIGN=MIDDLE  ALT=\"2x-3=2x%2B8-5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=-3x%2B12 ALIGN=MIDDLE  ALT=\"2x-3=-3x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-3x%2B12%2B3 ALIGN=MIDDLE  ALT=\"2x=-3x%2B12%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3x=12%2B3 ALIGN=MIDDLE  ALT=\"2x%2B3x=12%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=12%2B3 ALIGN=MIDDLE  ALT=\"5x=12%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=15 ALIGN=MIDDLE  ALT=\"5x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2815%29%2F%285%29 ALIGN=MIDDLE  ALT=\"x=%2815%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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