document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855779>Question 855779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch a graph of the solution of the system of linear inequalities.<BR>\n" );
document.write( "y&#8805;1/2x+1/2<BR>\n" );
document.write( "y&#8804;4x&#8722;1/2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515557 by </B><A HREF=/tutors/aboutme.mpl?userid=brysca><B>brysca(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=brysca><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/cgi-bin/show-face.mpl?user=brysca><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When graphed, both linear inequalities should look like this: \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+-4%2C+10%2C+-4%2C+10%2C+%28.5%2Ax%29%2B.5%2C+4x-.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-4%2C+10%2C+%28.5%2Ax%29%2B.5%2C+4x-.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To graph both inequalities manually, follow the expression y=mx+b where m is the slope (rise/run), and b is the y intercept.\r<BR>\n" );
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document.write( "To determine the solution set between the two graphs, we must put a test point.<BR>\n" );
document.write( "We will use point (0,0) for this example\r<BR>\n" );
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document.write( "Red graph:<BR>\n" );
document.write( "y &#8805; .5x+.5<BR>\n" );
document.write( "0 &#8805; .5(0)+.5<BR>\n" );
document.write( "0 &#8805; .5<BR>\n" );
document.write( "Is zero greater than .5? Of course not, so shade the upper side of the red graph\r<BR>\n" );
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document.write( "Green graph:<BR>\n" );
document.write( "y &#8804;4x&#8722;.5<BR>\n" );
document.write( "0 &#8804; 4(0)-.5<BR>\n" );
document.write( "0 &#8804; -.5<BR>\n" );
document.write( "Is zero less than -.5? No. So shade the right side of the green graph. <BR>\n" );
document.write( "Now, knowing the solution set for green graph and the red graph, just shade in the sides they have in common.<BR>\n" );
document.write( "In this problem, the shaded area should be in the middle of both of the graphs. </SPAN>\n" );
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