document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178782>Question 178782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve.\r<BR>\n" );
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document.write( "(x+13)(x-6)(x+5)>0\r<BR>\n" );
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document.write( "Use at least one inequality or compound inequality to express your answer.  For answers with more than one inequality, separate the inequalities by a comma. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133773 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=133773\">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( "First determine the three values that would make the expression on the left equal to zero, namely:  -13, -5, and 6\r<BR>\n" );
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document.write( "Plot these three points on the number line and notice that you have partitioned the number line into 4 regions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x < -13\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -13 < x < -5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5 < x < 6\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x > 6\">\r<BR>\n" );
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document.write( "Note that all of the inequality signs exclude equals because if x were equal to any of the three values, the value of the expression would be zero and the relation greater than zero would fail.\r<BR>\n" );
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document.write( "Now, from each of the four regions, select a value.  It doesn't matter what value, as long as it is in the specified interval and does not equal one of the partition points.\r<BR>\n" );
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document.write( "First, select something in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x < -13\">, say -15.  If -15 is substituted for <i>x</i> in the original inequality, the relationship fails because all three factors will be negative making the left side negative and therfore not greater than zero. This interval is excluded from the solution set.\r<BR>\n" );
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document.write( "Select something in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -13 < x < -5\">, say -10.  If -10 is substituted for <i>x</i>, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x + 13 = 3\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x -6 =  -16\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x + 5 = -5\">.  One positive factor and two negative factors means the product is positive and therefore greater than zero.  This interval is included in the solution set.\r<BR>\n" );
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document.write( "Using the same process to discover that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5 < x < 6\"> is excluded and and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x > 6\"> is included.\r<BR>\n" );
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document.write( "Solution set:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{x|x \in \R, -13 < x < -5, x > 6\}\">\r<BR>\n" );
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document.write( "Below is a graph of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = (x + 13)(x - 6)(x + 5)\">.  Note the portions of the graph that are above the x-axis.\r<BR>\n" );
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