document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134556>Question 134556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the additve inverse of a number divided  by twelve is the same as one less than three times its reciprocal. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98438 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=98438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number, then the additive inverse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a ALIGN=MIDDLE  ALT=\"-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and its reciprocal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa ALIGN=MIDDLE  ALT=\"1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \"is the same as\" means \"equals\"\r<BR>\n" );
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document.write( "The additive inverse of a number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a ALIGN=MIDDLE  ALT=\"-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >), divided by 12 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2F12 ALIGN=MIDDLE  ALT=\"-a%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is the same as (=) one less than (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) three times its reciprocal (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%281%2Fa%29=3%2Fa ALIGN=MIDDLE  ALT=\"3%2A%281%2Fa%29=3%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >).  Put it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2F12=%283%2Fa%29-1 ALIGN=MIDDLE  ALT=\"-a%2F12=%283%2Fa%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 1 to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-a%2F12=3%2Fa ALIGN=MIDDLE  ALT=\"1-a%2F12=3%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "LCD on the left is 12, so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812-a%29%2F12=3%2Fa ALIGN=MIDDLE  ALT=\"%2812-a%29%2F12=3%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cross-multiply (numerator on the left times denominator on the right equals denominator on the left times numerator on the right)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2812-a%29=36 ALIGN=MIDDLE  ALT=\"a%2812-a%29=36\"   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=12a-a%5E2=36 ALIGN=MIDDLE  ALT=\"12a-a%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%5E2%2B12a-36=0 ALIGN=MIDDLE  ALT=\"-a%5E2%2B12a-36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by -1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-12a%2B36=0 ALIGN=MIDDLE  ALT=\"a%5E2-12a%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Trinomial is a perfect square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-6%29%28a-6%29=0 ALIGN=MIDDLE  ALT=\"%28a-6%29%28a-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%286%29%2F12=%283%2F6%29-1 ALIGN=MIDDLE  ALT=\"-%286%29%2F12=%283%2F6%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2=1%2F2-1=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2=1%2F2-1=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Answer checks. </SPAN>\n" );
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