document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553110>Question 553110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%2F%28x%5E2-1%29+%3E=+-3+ ALIGN=MIDDLE  ALT=\"+2+%2F%28x%5E2-1%29+%3E=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Include a sketch to support answer.\r<BR>\n" );
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document.write( "I isolated x to get<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28+3+%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt+%28+3+%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28+3+%29%2F3 ALIGN=MIDDLE  ALT=\"-sqrt%28+3+%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > but I don't understand how x is greater than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%283%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt+%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and less than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28+3+%29%2F3 ALIGN=MIDDLE  ALT=\"-sqrt%28+3+%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I also don't know how to do the sketch.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360688 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{x^2\ -\ 1}\ \geq\ -3\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\ -\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ \geq\ -3\left(x^2\ -\ 1\right)\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{1}{3}\">.  Don't forget to reverse the sense of the inequality because of multiplying by a number less than zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 1\ \geq\ -\frac{2}{3}\">\r<BR>\n" );
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document.write( "Add 1 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ \geq\ \frac{1}{3}\">\r<BR>\n" );
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document.write( "Now when you take the root of bothsides, recognize that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ |x|\ \geq\ \frac{\sqrt{3}}{3}\">\r<BR>\n" );
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document.write( "Which is to say that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ \geq\ \frac{sqrt{3}}{3}\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ \leq\ -\frac{sqrt{3}}{3}\">\r<BR>\n" );
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document.write( "Draw a number line.  Put a filled in dot at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{sqrt{3}}{3}\">.  Make a fat arrow going to the right with an arrowhead indicating it goes on forever.  Put a filled in dot at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{sqrt{3}}{3}\">.  Make a fat arrow going to the left with an arrowhead indicating it goes on forever.  \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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