document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642887>Question 642887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When graphing the inequality 3x-2y&#8805; 0, why can’t we use (0, 0) as a test point/ If we test the point (-4, 2), do we obtain a false statement or true one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404264 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=404264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y+%3E=0 ALIGN=MIDDLE  ALT=\"3x-2y+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
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document.write( "that inequality simplifies to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%3E=+2y ALIGN=MIDDLE  ALT=\"3x+%3E=+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%3C=3x+ ALIGN=MIDDLE  ALT=\"2y%3C=3x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=%283%2F2%29x+ ALIGN=MIDDLE  ALT=\"y%3C=%283%2F2%29x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=boundary ALIGN=MIDDLE  ALT=\"boundary\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the inequality is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%283%2F2%29x ALIGN=MIDDLE  ALT=\"y+=+%283%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=on ALIGN=MIDDLE  ALT=\"on\"   DISABLED_style= \"max-width:90%; height:auto;\" > the boundary line.  It <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfies ALIGN=MIDDLE  ALT=\"satisfies\"   DISABLED_style= \"max-width:90%; height:auto;\" > the<BR>\n" );
document.write( "equality but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cannot ALIGN=MIDDLE  ALT=\"cannot\"   DISABLED_style= \"max-width:90%; height:auto;\" > be used to test the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=because ALIGN=MIDDLE  ALT=\"because\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=on+ ALIGN=MIDDLE  ALT=\"on+\"   DISABLED_style= \"max-width:90%; height:auto;\" >the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=boundary ALIGN=MIDDLE  ALT=\"boundary\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "You have to use a test point that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=boundary ALIGN=MIDDLE  ALT=\"boundary\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=%283%2F2%29%28-4%29+ ALIGN=MIDDLE  ALT=\"2%3C=%283%2F2%29%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=%283%2A%28-4%29%2F2%29+ ALIGN=MIDDLE  ALT=\"2%3C=%283%2A%28-4%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=%28-12%29%2F2%29+ ALIGN=MIDDLE  ALT=\"2%3C=%28-12%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=-6+ ALIGN=MIDDLE  ALT=\"2%3C=-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=true ALIGN=MIDDLE  ALT=\"true\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the half-plane does containing (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > the solution set for the inequality.\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=plot_any_inequality.solver>Plot Any Inequality</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Graphing function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=%283%2F2%29x ALIGN=MIDDLE  ALT=\"y%3C=%283%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=%283%2F2%29x+%29 ALIGN=MIDDLE  ALT=\"graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=%283%2F2%29x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "as you can see (when you plot it) this point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > the solution set for the inequality\r<BR>\n" );
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document.write( " </SPAN>\n" );
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