document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120785>Question 1120785</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there!<BR>\n" );
document.write( "I'm having a tough time trying to figure out how to solve the following rational inequality. \r<BR>\n" );
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document.write( "(x+2)/(x-4)<3\r<BR>\n" );
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document.write( "All of my teachers examples have big charts and graphs at the bottom of each solution (an interval chart I believe?) And I really do not understand the chart. \r<BR>\n" );
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document.write( "Anyways if anyone knows what this chart is and how I would go about solving the equation like that you would be a total life saver! Thanks so much in advance.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736478 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=736478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Multiply both sides of the inequality by the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 2\ <\ 3x\ -\ 12\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -2x\ <\ -14\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ >\ 7\">\r<BR>\n" );
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document.write( "Thus <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 7\"> is one critical point.  Other critical points are where the function is not defined, i.e. where the denominator is zero. In this case at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 4\">\r<BR>\n" );
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document.write( "With two critical points we divide the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-axis into three open intervals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (-\infty,4), (4,7), (7,\infty)\">\r<BR>\n" );
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document.write( "Choose a value from each interval that is NOT an end point:  I choose 3, 5, and 8\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(3)\ +\ 2}{3\ -\ 4}\ =\ \frac{5}{-1}\ <\ 3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(5)\ +\ 2}{5\ -\ 4}\ =\ \frac{7}{1}\ >\ 3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(8)\ +\ 2}{8\ -\ 4}\ =\ \frac{10}{4}\ <\ 3\">\r<BR>\n" );
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document.write( "Thus the solution set is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\ \in\ \mathbb{R}\ |\ -\infty\ <\ x\ <\ 4\ \text{or}\ 7\ <\ x\ <\ \infty}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=rationalinequality.jpg\">.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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