document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150538>Question 150538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was wondering if someone could explain how to shade linear equalities when you graph them. I know how to graph, I'm just confused on where to shade. <BR>\n" );
document.write( "3y + x > 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110501 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=110501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2Bx%3E4 ALIGN=MIDDLE  ALT=\"3y%2Bx%3E4\"   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%3E4-x ALIGN=MIDDLE  ALT=\"3y%3E4-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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%3E%284-x%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y%3E%284-x%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%3E%284%29%2F3-%28x%29%2F%283%29 ALIGN=MIDDLE  ALT=\"y%3E%284%29%2F3-%28x%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%3E-%281%2F3%29x%2B4%2F3\"   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%2Bx%3E4 ALIGN=MIDDLE  ALT=\"3y%2Bx%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%3E-%281%2F3%29x%2B4%2F3\"   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=-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%29x%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > first. \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-%281%2F3%29x%2B4%2F3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%29x%2B4%2F3\"   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-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%3E-%281%2F3%29x%2B4%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%3E-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%3E-%281%2F3%29x%2B4%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=0%3E-%281%2F3%29%2A%280%29%2B4%2F3 ALIGN=MIDDLE  ALT=\"0%3E-%281%2F3%29%2A%280%29%2B4%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=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%2F3 ALIGN=MIDDLE  ALT=\"0%3E4%2F3\"   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-%281%2F3%29x%2B4%2F3%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B0%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B0.666666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B1.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B2%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B2.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B3.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B4%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B4.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B5.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B6%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B6.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B7.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B8%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B8.66666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B9.33333333333333%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B10%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B10.6666666666667%29%2C%0D%0Agraph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F3%29x%2B4%2F3%2C-%281%2F3%29x%2B4%2F3%2B11.3333333333333%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-%281%2F3%29x%2B4%2F3 ALIGN=MIDDLE  ALT=\"y%3E-%281%2F3%29x%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2Bx%3E4 ALIGN=MIDDLE  ALT=\"3y%2Bx%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > )with the shaded region in green\r<BR>\n" );
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document.write( "Note: Since the inequality has a greater than sign \">\", this means that the red boundary line should be dotted since we are not including this line with the solution set.<BR>\n" );
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