document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74717>Question 74717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the following inequalities.\r<BR>\n" );
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document.write( "4x + y \"this symbol >  with one line under it\" 4<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 #53732 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=53732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+y+%3E=+4 ALIGN=MIDDLE  ALT=\"4x+%2B+y+%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's begin by just making this expression and equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+y+=+4 ALIGN=MIDDLE  ALT=\"4x+%2B+y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now graph this equation.  Because the variables x and y have an understood exponent 1 you<BR>\n" );
document.write( "can recognize this as a first degree linear equation.  The graph is a straight line.  <BR>\n" );
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document.write( "You can easily graph the equation by first letting x equal zero.  When you do, the equation <BR>\n" );
document.write( "reduces to y = 4. So (0, 4) is on point on the graph. Next, let y = 0.  When you do the equation<BR>\n" );
document.write( "reduces to 4x = 4 and dividing both sides of that equation by 4 you get x = 1.  So the point<BR>\n" );
document.write( "(1, 0) is also on the graph.  If you want more points, just assign other values to x and<BR>\n" );
document.write( "solve the original equation for y.  This will give you more points to confirm that you<BR>\n" );
document.write( "have the correct line.<BR>\n" );
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document.write( "After plotting these points, take a straight edge and run a line through them.  This is the<BR>\n" );
document.write( "graph of the equation 4x + y = 4.<BR>\n" );
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document.write( "What does that mean? The graph represents the x,y points where 4x + y = 4.  But the original<BR>\n" );
document.write( "problem not only said that 4x + y = 4. It said that 4x + y is greater than 4.  That means<BR>\n" );
document.write( "that any x,y points that are above that graph will make 4x + y greater than 4. You can represent<BR>\n" );
document.write( "that by shading the area above the line. The (x,y) points in that shaded area will make<BR>\n" );
document.write( "4x + y greater than 4.<BR>\n" );
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document.write( "So the answer is that any (x,y) point on the graph or in the shaded area above the graph <BR>\n" );
document.write( "satisfy the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+y+%3E=+4 ALIGN=MIDDLE  ALT=\"4x+%2B+y+%3E=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Hope this helps you to understand problems of this type.  You can treat them like equations,<BR>\n" );
document.write( "with the exception that if you multiply or divide both sides of the inequality by a NEGATIVE<BR>\n" );
document.write( "number, you must flip the inequality sign to point in the opposite direction. We did not<BR>\n" );
document.write( "have to do that for this problem.<BR>\n" );
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