document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146656>Question 146656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph the inequality on a plane<BR>\n" );
document.write( "3y-4x>12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107082 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=107082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-4x%3E12 ALIGN=MIDDLE  ALT=\"3y-4x%3E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-4x=12 ALIGN=MIDDLE  ALT=\"3y-4x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the inequality sign with an equals sign.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=12%2B4x ALIGN=MIDDLE  ALT=\"3y=12%2B4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2812%2B4x%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y=%2812%2B4x%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So in order to plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-4x%3E12 ALIGN=MIDDLE  ALT=\"3y-4x%3E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3E%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the same thing), we need to plot the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > first. <BR>\n" );
document.write( "(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+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in a test point (0,0) into the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3E%284%2F3%29x%2B4\"   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=y%3E%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3E%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E%284%2F3%29%2A%280%29%2B4 ALIGN=MIDDLE  ALT=\"0%3E%284%2F3%29%2A%280%29%2B4\"   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%3E4 ALIGN=MIDDLE  ALT=\"0%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify.\r<BR>\n" );
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document.write( "Since the inequality is false, this means that we shade the entire region that does <b>NOT</b> contain the point (0,0)\r<BR>\n" );
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document.write( "In other words, we simply shade the <b>entire</b> region that is above the line.\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+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B0%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B2.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B5.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B8%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B10.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B13.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B16%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B18.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B21.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B24%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B26.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B29.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B32%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B34.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B37.3333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B40%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B42.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%284%2F3%29x%2B4%2C%284%2F3%29x%2B4%2B45.3333333333333%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%284%2F3%29x%2B4 ALIGN=MIDDLE  ALT=\"y%3E%284%2F3%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in green\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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