document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82579>Question 82579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of linear inequalities by graphing:\r<BR>\n" );
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document.write( "x-2y<4<BR>\n" );
document.write( "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 #59154 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=59154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the first equation for y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y%3C4 ALIGN=MIDDLE  ALT=\"x-2y%3C4\"   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=-2y%3C4-x ALIGN=MIDDLE  ALT=\"-2y%3C4-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract x 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%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y%3E%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -2. Remember multiplying or dividing by a negative flips the inequality sign\r<BR>\n" );
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document.write( "Now graph both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%281%2F2%29x-2%2C+10000%28x-4%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%281%2F2%29x-2%2C+10000%28x-4%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets pick a test point (0,0) and test it with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y%3E%281%2F2%29x-2\"   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=%280%29%3E%281%2F2%29%280%29-2 ALIGN=MIDDLE  ALT=\"%280%29%3E%281%2F2%29%280%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0, y=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E-2 ALIGN=MIDDLE  ALT=\"0%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since this expression is true we shade the entire region containing (0,0) for the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y%3E%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This region is above the line.\r<BR>\n" );
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document.write( "Now lets test <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   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=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C4 ALIGN=MIDDLE  ALT=\"0%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since this expression is true we shade the entire region containing (0,0) for the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is the region to the left of the vertical line.\r<BR>\n" );
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document.write( "Notice how these regions overlap. This overlapping region is our final shaded region. Every point in this region satisfies both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%281%2F2%29x-2 ALIGN=MIDDLE  ALT=\"y%3E%281%2F2%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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