document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151858>Question 151858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to graph the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%3E+x%2F3+ ALIGN=MIDDLE  ALT=\"+y+%3E+x%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I dont understand how to simplify the inequality towards where I can graph it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111639 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=111639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, graph the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F3 ALIGN=MIDDLE  ALT=\"y=x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: the equation is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x\"   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=+drawing%28500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0A+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%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=x%2F3 ALIGN=MIDDLE  ALT=\"y=x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's pick a test point (that's not on the line), say (0,1) and plug it into the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3Ex%2F3 ALIGN=MIDDLE  ALT=\"y%3Ex%2F3\"   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%3Ex%2F3 ALIGN=MIDDLE  ALT=\"y%3Ex%2F3\"   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=1%3E0%2F3 ALIGN=MIDDLE  ALT=\"1%3E0%2F3\"   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=1 ALIGN=MIDDLE  ALT=\"y=1\"   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=1%3E0 ALIGN=MIDDLE  ALT=\"1%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since the inequality is true, this means that we shade the <font size=4><b>entire</b></font> region that the point (0,1) is in. So we simply shade everything above the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F3 ALIGN=MIDDLE  ALT=\"y=x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\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%281%2F3%29x%2C%281%2F3%29x%2B3%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B6%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B9%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B12%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B15%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B18%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B21%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B24%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B27%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B30%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B33%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B36%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B39%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B42%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B45%29%2C%0D%0Agraph%28++500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%281%2F3%29x%2C%281%2F3%29x%2B48%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=y%3Ex%2F3 ALIGN=MIDDLE  ALT=\"y%3Ex%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in green </SPAN>\n" );
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