document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85721>Question 85721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the inequality.<BR>\n" );
document.write( "	x <= 5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61924 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=61924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20.\r<BR>\n" );
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document.write( "Start with the given system of inequalities\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=5 ALIGN=MIDDLE  ALT=\"x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In order to graph this system of inequalities, we need to graph each inequality one at a time.\r<BR>\n" );
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document.write( "So lets graph the first inequality\r<BR>\n" );
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document.write( "    In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=5 ALIGN=MIDDLE  ALT=\"x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need to graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace the inequality sign with an equal sign). So lets graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C1000%28x-5000%2F1000%29%29 ALIGN=MIDDLE  ALT=\"graph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C1000%28x-5000%2F1000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=5 ALIGN=MIDDLE  ALT=\"x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%3C=5 ALIGN=MIDDLE  ALT=\"%280%29%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0, y=0\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=5 ALIGN=MIDDLE  ALT=\"0%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since this inequality is true, we shade the entire region containing (0,0)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2Cgraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B0%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B0.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B1.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B2.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B3%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B3.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B4.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B5.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B6%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B6.75%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B7.5%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B8.25%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B9%29%29%2C%0D%0Agraph%28+400%2C+300%2C+-5%2C+10%2C+-10%2C+10%2C10000%28x-5000%2F1000%29%2C+10000%28x-5000%2F1000%2B9.75%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Here is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=5 ALIGN=MIDDLE  ALT=\"x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the graph of the line(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) in red and the shaded region in green \r<BR>\n" );
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document.write( "(note: In this case, the red line is a solid line. This means the boundaries are included in the region.)<BR>\n" );
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