document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315244>Question 315244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me set up and solve this problem.  The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24. What is the integer?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225559 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The reciprocal of twice an integer added to the reciprocal of two more than twice the integer is 7/24.<BR>\n" );
document.write( " What is the integer?<BR>\n" );
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document.write( "Let x = the integer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282x%2B2%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%282x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F24 ALIGN=MIDDLE  ALT=\"7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 24x(2x+2)<BR>\n" );
document.write( "24x(2x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282x%29 ALIGN=MIDDLE  ALT=\"1%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 24x(2x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282x%2B2%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%282x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 24x(2x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F24 ALIGN=MIDDLE  ALT=\"7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel the denominators, results:<BR>\n" );
document.write( "12(2x+2) + 24x = 7x(2x+2)<BR>\n" );
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document.write( "24x + 24 + 24x = 14x^2 + 14x<BR>\n" );
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document.write( "48x + 24 = 14x^2 + 14x<BR>\n" );
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document.write( "Combine on the right<BR>\n" );
document.write( "0 = 14x^2 + 14x - 48x - 24<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "14x^2 - 34x - 24 = 0<BR>\n" );
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document.write( "simplify, divide by 2<BR>\n" );
document.write( "7x^2 - 17x - 12 = 0<BR>\n" );
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document.write( "factor this to<BR>\n" );
document.write( "(7x+4)(x-3) = 0<BR>\n" );
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document.write( "The positive solution is all we want here<BR>\n" );
document.write( "x = 3 is the integer, that everyone is waiting for!<BR>\n" );
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document.write( "See if this is true<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"1%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282%283%29%2B2%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%282%283%29%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F24 ALIGN=MIDDLE  ALT=\"7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F24 ALIGN=MIDDLE  ALT=\"7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F24 ALIGN=MIDDLE  ALT=\"4%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F24 ALIGN=MIDDLE  ALT=\"3%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F24 ALIGN=MIDDLE  ALT=\"7%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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