document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23316>Question 23316</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with this problem and its graph.\r<BR>\n" );
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document.write( "x-3/x+5 < 0\r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Marcus </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12093 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12093\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving inequalities can most easily be solved by graphing calculator methods.\r<BR>\n" );
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document.write( "First of all, did you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x%2B5%29+%3C0+ ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x%2B5%29+%3C0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or did you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%283%2Fx%29%2B5%3C0 ALIGN=MIDDLE  ALT=\"x-%283%2Fx%29%2B5%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  I think you probably meant the first.  I will solve this one, and if I have misinterpreted your problem, then either let me know by Email or re-post the problem and we'll give it another try.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%2F%28x%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"+%28x-3%29%2F%28x%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first step is to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+%28x-3%29%2F%28x%2B5%29+ ALIGN=MIDDLE  ALT=\"+y=+%28x-3%29%2F%28x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Because the problem says <0, you need to find all values of x for which the graph is BELOW THE X-AXIS!  If the problem had been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%2F%28x%2B5%29%3E0 ALIGN=MIDDLE  ALT=\"+%28x-3%29%2F%28x%2B5%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you would draw the same graph, but to solve this one, you need to find all values of x where the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=+%28x-3%29%2F%28x%2B5%29+ ALIGN=MIDDLE  ALT=\"+y=+%28x-3%29%2F%28x%2B5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is ABOVE THE Y-AXIS!  \r<BR>\n" );
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document.write( "So here is the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+%28x-3%29%2F%28x%2B5%29+%29+ ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+%28x-3%29%2F%28x%2B5%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that the graph crosses the x-axis at x= 3.  Notice that it looks like a vertical line at x=-5.  This is actually an ASYMPTOTE, which SHOULD be drawn with a DOTTED LINE.  An asymptote is a value of x where the graph will go off to infinity--it never quite gets to that value of x, which in this case is at x= -5.  Notice that this graph is BELOW THE X-AXIS from -5 to 3, so the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%3Cx%3C3 ALIGN=MIDDLE  ALT=\"-5%3Cx%3C3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Interval notation for this problem will be (-5,3).  \r<BR>\n" );
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document.write( "This may not have been what you were expecting in a problem.  I think it's MUCH easier than the old ways that I used to teach.  \r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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