document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151741>Question 151741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve and graph an inequalitie like x - 2 > 2x + 1 or -10 > -2x - 2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111548 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=111548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%3E2x%2B1 ALIGN=MIDDLE  ALT=\"x-2%3E2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%3E2x%2B1 ALIGN=MIDDLE  ALT=\"x-2%3E2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E2x%2B1%2B2 ALIGN=MIDDLE  ALT=\"x%3E2x%2B1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2x%3E1%2B2 ALIGN=MIDDLE  ALT=\"x-2x%3E1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E1%2B2 ALIGN=MIDDLE  ALT=\"-x%3E1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E3 ALIGN=MIDDLE  ALT=\"-x%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%283%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x%3C%283%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-3 ALIGN=MIDDLE  ALT=\"x%3C-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Now let's solve the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%3E-2x-2 ALIGN=MIDDLE  ALT=\"-10%3E-2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%3E-2x-2 ALIGN=MIDDLE  ALT=\"-10%3E-2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3E-2x-2%2B10 ALIGN=MIDDLE  ALT=\"0%3E-2x-2%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3E-2%2B10 ALIGN=MIDDLE  ALT=\"2x%3E-2%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%3E8 ALIGN=MIDDLE  ALT=\"2x%3E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E%288%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x%3E%288%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E4 ALIGN=MIDDLE  ALT=\"x%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-3 ALIGN=MIDDLE  ALT=\"x%3C-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <font size=\"4\"><b>or</b></font>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E4 ALIGN=MIDDLE  ALT=\"x%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solution in interval notation is: <font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-\infty,-3}\"><font size=\"8\">)</font> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cup\"><font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{4,\infty}\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( "So the solution in set notation is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|x<-3 \textrm{..or..} x>4\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C-8%2C+9%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-8%2C+9+%29%2C%0D%0A%0D%0A%0D%0Acircle%28-3%2C0%2C0.25%29%2C%0D%0Acircle%28-3%2C0%2C0.20%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%28-3%2C0%2C-8%2C0%29%29%2C%0D%0Ablue%28arrow%28-3%2C0.30%2C-8%2C0.30%29%29%2C%0D%0Ablue%28arrow%28-3%2C0.15%2C-8%2C0.15%29%29%2C%0D%0Ablue%28arrow%28-3%2C-0.15%2C-8%2C-0.15%29%29%2C%0D%0Ablue%28arrow%28-3%2C-0.30%2C-8%2C-0.30%29%29%2C%0D%0A%0D%0A%0D%0A%0D%0Acircle%284%2C0%2C0.25%29%2C%0D%0Acircle%284%2C0%2C0.20%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%284%2C0%2C9%2C0%29%29%2C%0D%0Ablue%28arrow%284%2C0.30%2C9%2C0.30%29%29%2C%0D%0Ablue%28arrow%284%2C0.15%2C9%2C0.15%29%29%2C%0D%0Ablue%28arrow%284%2C-0.15%2C9%2C-0.15%29%29%2C%0D%0Ablue%28arrow%284%2C-0.30%2C9%2C-0.30%29%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note:\r<BR>\n" );
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document.write( "There is an <b>open</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding that value from the solution set.\r<BR>\n" );
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document.write( "Also, there is an <b>open</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding that value from the solution set.\r<BR>\n" );
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