document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421517>Question 421517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just dont get how to graph inequality. <BR>\n" );
document.write( "Graph the inequality x< -3y<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 #294360 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=294360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to graph any equation, you need to solve for y.\r<BR>\n" );
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document.write( "then you need to graph the equality.\r<BR>\n" );
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document.write( "then you need to determine the area of the inequality.\r<BR>\n" );
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document.write( "your equation is x < -3y\r<BR>\n" );
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document.write( "add 3y to both sides of the equation and subtract x from both sides of the equation to get:\r<BR>\n" );
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document.write( "3y < -x\r<BR>\n" );
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document.write( "divide both sides of the equation by 3 to get:\r<BR>\n" );
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document.write( "y < -x/3\r<BR>\n" );
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document.write( "that's your inequality after you solved for y.\r<BR>\n" );
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document.write( "now graph the equality.\r<BR>\n" );
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document.write( "the equality is y = -x/3\r<BR>\n" );
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document.write( "this is what you graph.\r<BR>\n" );
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document.write( "your graph will 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%28600%2C600%2C-5%2C5%2C-5%2C5%2C-x%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2C-x%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when you look at this graph, you see that the line is all points where y = -x/3.\r<BR>\n" );
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document.write( "now look at your inequality equation.\r<BR>\n" );
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document.write( "that is y < -x/3\r<BR>\n" );
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document.write( "in order for the value of y to be smaller than -x/3 for any value of x, you will need to be in the area of the graph that is beneath the line.\r<BR>\n" );
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document.write( "you would shade that area to indicate that the solution to the equation of y < -x/3 is in that area.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 3, the value of the equation of the line y = -x/3 becomes -1.\r<BR>\n" );
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document.write( "you can see that the value of y = -1 when x = 3 is on the line.\r<BR>\n" );
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document.write( "the value of y for the equation of y < -x/3 would have to be less than -1 which would place it in the area below the line.\r<BR>\n" );
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document.write( "the graph you create will look like the graph i showed you except you would have shaded the area below the line to indicate that is where the solution to the inequality lies.\r<BR>\n" );
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document.write( "unlike an equality solution, the inequality solution will contain many values of y that are less than the value of -x/3.\r<BR>\n" );
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document.write( "all those possible solutions will be in the shaded area.\r<BR>\n" );
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