document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144161>Question 144161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i graph inequalities\r<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 #104931 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph an inequality, treat the <, &#8804;, >, or &#8805; sign as an = sign, and graph the equation. \r<BR>\n" );
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document.write( "If you are given the inequality with < or > sign, graph the equation as a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dotted ALIGN=MIDDLE  ALT=\"dotted\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If the inequality is &#8804; or &#8805;, graph the equation as a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=solid ALIGN=MIDDLE  ALT=\"solid\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "This line divides the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-+plane ALIGN=MIDDLE  ALT=\"xy-+plane\"   DISABLED_style= \"max-width:90%; height:auto;\" > into two regions: a region that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfies ALIGN=MIDDLE  ALT=\"satisfies\"   DISABLED_style= \"max-width:90%; height:auto;\" > the inequality, and a region that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+not ALIGN=MIDDLE  ALT=\"+not\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Next, pick a point not on the line. Check to see if this point satisfies the inequality. <BR>\n" );
document.write( "If it satisfies the inequality, shade the region which contains that point. <BR>\n" );
document.write( "If it does not satisfy the inequality, shade the region which does not contain that point. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=All ALIGN=MIDDLE  ALT=\"All\"   DISABLED_style= \"max-width:90%; height:auto;\" >the points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in ALIGN=MIDDLE  ALT=\"in\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+the+ ALIGN=MIDDLE  ALT=\"+the+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shaded ALIGN=MIDDLE  ALT=\"shaded\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+region ALIGN=MIDDLE  ALT=\"+region\"   DISABLED_style= \"max-width:90%; height:auto;\" > will <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=satisfy ALIGN=MIDDLE  ALT=\"satisfy\"   DISABLED_style= \"max-width:90%; height:auto;\" > the inequality. <BR>\n" );
document.write( "Note: The origin (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is usually the easiest point to test, provided it is not on the line.<BR>\n" );
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