document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102656>Question 102656</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073268620/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please Help!\r<BR>\n" );
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document.write( "Graph the inequality and shade in the correct area of the graph:\r<BR>\n" );
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document.write( "2/3x + 3y 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 #74676 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=74676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x+%2B+3y+%3C=12 ALIGN=MIDDLE  ALT=\"%282%2F3%29x+%2B+3y+%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=2x+%2B+9y+%3C=36 ALIGN=MIDDLE  ALT=\"2x+%2B+9y+%3C=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 3 to eliminate any fractions\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%2B9y%3C=36 ALIGN=MIDDLE  ALT=\"2x%2B9y%3C=36\"   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%2B9y=36 ALIGN=MIDDLE  ALT=\"2x%2B9y=36\"   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%2B9y=36 ALIGN=MIDDLE  ALT=\"2x%2B9y=36\"   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%2F9%29x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+-%282%2F9%29x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B9y=36 ALIGN=MIDDLE  ALT=\"2x%2B9y=36\"   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, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B9y%3C=36 ALIGN=MIDDLE  ALT=\"2x%2B9y%3C=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the test point\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%2B9%280%29%3C=36 ALIGN=MIDDLE  ALT=\"2%280%29%2B9%280%29%3C=36\"   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=36 ALIGN=MIDDLE  ALT=\"0%3C=36\"   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%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-1.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-4.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-7.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-10.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-13.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-16.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-19.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-22.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-25.5%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%282%2F9%29x%2B4%2C-%282%2F9%29x%2B4%2B-28.5%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%2B9y%3C=36 ALIGN=MIDDLE  ALT=\"2x%2B9y%3C=36\"   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%2B9y=36 ALIGN=MIDDLE  ALT=\"2x%2B9y=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > in red) and the shaded region (in green) \r<BR>\n" );
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document.write( " </SPAN>\n" );
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