document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146778>Question 146778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph inequality.<BR>\n" );
document.write( "3x+4y is less than 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 #107190 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=107190\">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=3x%2B4y%3C=12 ALIGN=MIDDLE  ALT=\"3x%2B4y%3C=12\"   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=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=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=4y=12-3x ALIGN=MIDDLE  ALT=\"4y=12-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2812-3x%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y=%2812-3x%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%283%2F4%29x%2B3\"   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=3x%2B4y%3C=12 ALIGN=MIDDLE  ALT=\"3x%2B4y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y%3C=-%283%2F4%29x%2B3\"   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=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%283%2F4%29x%2B3\"   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-%283%2F4%29x%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%283%2F4%29x%2B3\"   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%3C=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y%3C=-%283%2F4%29x%2B3\"   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%3C=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y%3C=-%283%2F4%29x%2B3\"   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%3C=-%283%2F4%29%2A%280%29%2B3 ALIGN=MIDDLE  ALT=\"0%3C=-%283%2F4%29%2A%280%29%2B3\"   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=3 ALIGN=MIDDLE  ALT=\"0%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify.\r<BR>\n" );
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document.write( "Since the inequality is true, this means that we shade the entire region that contains 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 below 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-%283%2F4%29x%2B3%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-0%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-1.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-4.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-7.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-10.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-13.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-16.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-19.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-22.5%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%283%2F4%29x%2B3%2C-%283%2F4%29x%2B3-24%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%3C=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y%3C=-%283%2F4%29x%2B3\"   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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