document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72931>Question 72931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the inequality.<BR>\n" );
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document.write( "    3x + y &#8804; 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52268 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=52268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+y+%3C=+5 ALIGN=MIDDLE  ALT=\"3x+%2B+y+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Graph this expression.<BR>\n" );
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document.write( "Begin by assuming this is an equation and let's get it into the slope intercept form.<BR>\n" );
document.write( "By assuming it's an equation we can operate on it in the normal way of applying mathematical<BR>\n" );
document.write( "operations.  The only thing we have to be careful of is if we multiply or divide both sides<BR>\n" );
document.write( "of our \"equation\" by a negative number we have to reverse the direction of the inequality<BR>\n" );
document.write( "sign.  <BR>\n" );
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document.write( "The next thing we can do is subtract 3x from both sides to eliminate the 3x on the left side.<BR>\n" );
document.write( "The result of this is that the \"equation\" becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=-3x+%2B+5 ALIGN=MIDDLE  ALT=\"y+%3C=-3x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You may now recognize that this is in slope-intercept form.  The graph intercepts the<BR>\n" );
document.write( "y-axis at +5 and the slope is down and to the right (because the slope is negative)<BR>\n" );
document.write( "at a rate of -3 ... meaning that for every one unit the graph goes to the right, it goes down <BR>\n" );
document.write( "3 units in the vertical direction.<BR>\n" );
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document.write( "Graph this line.  When you do it should look like:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C+-20%2C20%2C-3x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C+-20%2C20%2C-3x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next what you want to do is to shade in the area below the graphed line, and shade it<BR>\n" );
document.write( "so it includes the graphed line but nothing above it.  Now you can claim that any value<BR>\n" );
document.write( "of y that satisfies the original equality is in that shaded area (including on the graphed line)<BR>\n" );
document.write( "because that shaded area identifies where any point in that area has a y value that is less than <BR>\n" );
document.write( "or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+%2B5 ALIGN=MIDDLE  ALT=\"-3x+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as represented by the graphed line.<BR>\n" );
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document.write( "Hope that this process gives you some insight into how inequalities can be graphed. </SPAN>\n" );
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