document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87747>Question 87747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a tough question. Please Help.  Solve x/(x – 5) < 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63658 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=63658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve x/(x – 5) < 2<BR>\n" );
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document.write( "Rewrite as:<BR>\n" );
document.write( "[x/(x-5)] - 2 < 0\r<BR>\n" );
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document.write( "Rewrite with a common denominator:\r<BR>\n" );
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document.write( "[x/(x-5)] - [2(x-5)/(x-5)] <0\r<BR>\n" );
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document.write( "Combine the numerators: to get:<BR>\n" );
document.write( "[x-2(x-5)]/(x-5) < 0<BR>\n" );
document.write( "[-(x-10)]/[(x-5)] < 0<BR>\n" );
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document.write( "The numerator is zero when x=10<BR>\n" );
document.write( "The denominator is zero when x=5<BR>\n" );
document.write( "Both of these are NOT part of the solution.<BR>\n" );
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document.write( "Draw a number line; plot points x=5 and x=10<BR>\n" );
document.write( "This breaks the number line into three intervals.<BR>\n" );
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document.write( "Determine which interval(s) are part of the solution set:<BR>\n" );
document.write( "Pick a sample value from each interval and check it in the INEQUALITY, as follows:<BR>\n" );
document.write( "In the interval (-inf,5) pick x=0; then -(0-10)/(0-5)=-2 which is < 0<BR>\n" );
document.write( "Therefore all x values in that interval are part of the solution set.<BR>\n" );
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document.write( "In the interval (5,10) pick x = 8; then -(8-10)/(8-5)>0<BR>\n" );
document.write( "Therefore no values in that interval are part of the solution set.<BR>\n" );
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document.write( "In the interval (10,inf) pick x=100; then -(100-10)/(100-5)<0<BR>\n" );
document.write( "Therefore all x values in that interval are part of the solution set.<BR>\n" );
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document.write( "Conclusion:<BR>\n" );
document.write( "The solution is all x-values in (-inf,5) OR (10,inf)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-25%2C25%2C-5%2C5%2Cx%2F%28x-5%29%2C2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-25%2C25%2C-5%2C5%2Cx%2F%28x-5%29%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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