document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040380>Question 1040380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't understand the shading portion of this particular question that I have. It is 6x - y> -4 and -x + 4y less than or equal to 6. It wants me to graph and show what part of the graph needs to be shaded. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655217 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6x - y > -4<BR>\n" );
document.write( "-x + 4y <= 6\r<BR>\n" );
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document.write( "first you want to solve for y in both equations.\r<BR>\n" );
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document.write( "first inequality:<BR>\n" );
document.write( "start with 6x - y > -4<BR>\n" );
document.write( "subtract 6x from both sides of the equation to get -y > -4 - 6x.<BR>\n" );
document.write( "multiply both sides of the inequality by -1 to get y < 4 + 6x.<BR>\n" );
document.write( "reorder the terms in descending order of degree to get y < 6x + 4.<BR>\n" );
document.write( "note that multiplying or dividing both sides of an inequality by a negative number reverses the inequality.<BR>\n" );
document.write( "in this case we multiplied both sides of the inequality by a negative number.\r<BR>\n" );
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document.write( "your first inequality becomes y < 6x + 4.\r<BR>\n" );
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document.write( "second inequality:<BR>\n" );
document.write( "start with -x + 4y <= 6<BR>\n" );
document.write( "add x to both sides of the inequality to get 4y <= 6 + x.<BR>\n" );
document.write( "divide both sides of the inequality by 4 to get y <= (6+x)/4.<BR>\n" );
document.write( "reorder the terms in descending order of degree to get y <= (x+6)/4.\r<BR>\n" );
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document.write( "your second inequality becomes y <= (x+6)/4.\r<BR>\n" );
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document.write( "your inequalities are now:\r<BR>\n" );
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document.write( "y < 6x+4<BR>\n" );
document.write( "y <= (x+6)/4\r<BR>\n" );
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document.write( "you would graph the lines created by these inequalities.\r<BR>\n" );
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document.write( "in other words, you would graph:\r<BR>\n" );
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document.write( "y = 6x+4<BR>\n" );
document.write( "y = (x+6)/4\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/070802.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you would then shade the areas indicated by the inequalities.\r<BR>\n" );
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document.write( "y < 6x+4 would have the area underneath and to the right of it shaded.<BR>\n" );
document.write( "since the inequality is < rather than <=, you would create a dashed line rather than a solid line.\r<BR>\n" );
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document.write( "y <= (x+6)/4 would have the area underneath and to the right of it shaded.<BR>\n" );
document.write( "since the inequality is <=, you would create a solid line rather than a dashed line.\r<BR>\n" );
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document.write( "dashed line means the inequality does not include the line.<BR>\n" );
document.write( "solid line means the inequality does include the line as well.\r<BR>\n" );
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document.write( "here's the graph of the inequality.<BR>\n" );
document.write( "the darkest shaded area is the shaded area you would need to create manually.<BR>\n" );
document.write( "that becomes the region of feasibility.<BR>\n" );
document.write( "it is below the line of y = 6x + 4 but does not include that line.<BR>\n" );
document.write( "it is below the line of y = (x+6)/4 and does include that line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/070803.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a reference on graphing inequalities.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathsisfun.com/algebra/graphing-linear-inequalities.html\" target = \"_blank\">http://www.mathsisfun.com/algebra/graphing-linear-inequalities.html</a> </SPAN>\n" );
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