document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87406>Question 87406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the inequality:<BR>\n" );
document.write( "2x-3y is less then or equal to 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63516 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=63516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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=2x-3y%3C=12 ALIGN=MIDDLE  ALT=\"2x-3y%3C=12\"   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( "First lets graph the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%3C=12 ALIGN=MIDDLE  ALT=\"2x-3y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=2x-3y%3C=12 ALIGN=MIDDLE  ALT=\"2x-3y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to graph the <b>equation</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace the inequality sign with an equal sign).<BR>\n" );
document.write( "So lets graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   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+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%282%2F3%29x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%282%2F3%29x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   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=2x-3y%3C=12 ALIGN=MIDDLE  ALT=\"2x-3y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute (0,0) into the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29-3%280%29%3C=12 ALIGN=MIDDLE  ALT=\"2%280%29-3%280%29%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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=0%3C=12 ALIGN=MIDDLE  ALT=\"0%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since this inequality is true, we simply shade the entire region that contains (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+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B2%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B4%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B8%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B10%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B14%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B16%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B20%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B22%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B26%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B28%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B32%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B34%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%282%2F3%29x-4%2C%282%2F3%29x-4%2B38%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y%3C=12 ALIGN=MIDDLE  ALT=\"2x-3y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the boundary (which is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=12 ALIGN=MIDDLE  ALT=\"2x-3y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) \r<BR>\n" );
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