document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72886>Question 72886</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131400592/algebrahomeworkh>Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve and graph inequality # 24<BR>\n" );
document.write( "-x-2y>4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52144 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=52144\">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=-x-2y%3E4 ALIGN=MIDDLE  ALT=\"-x-2y%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "First solve this inequality for y.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Use the same method as you would use in solving an equation ... (for the time being you<BR>\n" );
document.write( "can sort of imagine that the > sign is an equal sign).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Begin by adding x to both sides to remove the -x from the left side.  When you do that the<BR>\n" );
document.write( "inequality becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2y+%3E+x+%2B+4 ALIGN=MIDDLE  ALT=\"+-2y+%3E+x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now to solve for y you divide both sides by -2. This results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E+x%2F%28-2%29+%2B+4%2F%28-2%29 ALIGN=MIDDLE  ALT=\"y+%3E+x%2F%28-2%29+%2B+4%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "At this point we have to take care of another inequality rule.  This rule says that whenever<BR>\n" );
document.write( "you divide or multiply by a negative number you also need to reverse the direction of <BR>\n" );
document.write( "the inequality sign.  We divided by negative 2, but we have not reversed the direction<BR>\n" );
document.write( "of the inequality sign. So let's do that before we forget it. The inequality becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+x%2F%28-2%29+%2B+4%2F%28-2%29 ALIGN=MIDDLE  ALT=\"y+%3C+x%2F%28-2%29+%2B+4%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Do the algebra on the right side to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C+%28-1%2F2%29%2Ax+-+2 ALIGN=MIDDLE  ALT=\"y+%3C+%28-1%2F2%29%2Ax+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's the solution you need.  Notice that if the \"<\" sign were replaced by an equal sign<BR>\n" );
document.write( "you would have an equation in the slope-intercept form.  The slope would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29 ALIGN=MIDDLE  ALT=\"-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the y-intercept would be -2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you graphed this equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29%2Ax+-+2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29%2Ax+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The graph would look like:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+%28-x%2F2%29+-2%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+%28-x%2F2%29+-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "How do we interpret this?  We know that the equation for this graph is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29%2Ax+-+2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29%2Ax+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "but when we add the inequality sign that we got, it tells us that y must be below this<BR>\n" );
document.write( "graph (or less than the graphed line, if you prefer).  So shade in everything below<BR>\n" );
document.write( "this line.  That shaded area is the region of all values of y that satisfy the inequality.<BR>\n" );
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document.write( "Note that y cannot be on the line because the inequality sign says \"less than\". If the sign<BR>\n" );
document.write( "was \"less than or equal to\" then y could be on the graphed line as well as below it.<BR>\n" );
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document.write( "Hope this helps you to understand a little more about solving inequalities and graphing them<BR>\n" );
document.write( "as well. </SPAN>\n" );
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