document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174989>Question 174989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the inequality x^2-2x<8 is equivalent to what? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130055 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=130055\">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%5E2-2x%3C8 ALIGN=MIDDLE  ALT=\"x%5E2-2x%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-8%3C0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 8 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-4%29%3C0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-4%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Factor the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the left side equal to zero\r<BR>\n" );
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document.write( "Set each individual factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Solve for x in each case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <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;\" > \r<BR>\n" );
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document.write( "So our critical values are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <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;\" > \r<BR>\n" );
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document.write( "Now set up a number line and plot the critical values on the number line\r<BR>\n" );
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document.write( "So let's pick some test points that are near the critical values and evaluate them.\r<BR>\n" );
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document.write( "Let's pick a test value that is less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how it's to the left of the leftmost endpoint):\r<BR>\n" );
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document.write( "So let's pick <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-8%3C0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2B2%29%28-3-4%29%3C+0 ALIGN=MIDDLE  ALT=\"%28-3%2B2%29%28-3-4%29%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%3C+0 ALIGN=MIDDLE  ALT=\"7%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
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document.write( "Since the inequality is false, this means that the interval does <b>not</b> work. So this interval is <b>not</b> in our solution set and we can ignore it.\r<BR>\n" );
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document.write( "Let's pick a test value that is in between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "So let's pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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%5E2-2x-8%3C0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B2%29%281-4%29%3C+0 ALIGN=MIDDLE  ALT=\"%281%2B2%29%281-4%29%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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=-9%3C+0 ALIGN=MIDDLE  ALT=\"-9%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
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document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r<BR>\n" );
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document.write( "   So part our solution in interval notation is <font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -2,4\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( "   \r<BR>\n" );
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document.write( "Let's pick a test value that is greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how it's to the right of the rightmost endpoint):\r<BR>\n" );
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document.write( "So let's pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   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%5E2-2x-8%3C0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B2%29%285-4%29%3C+0 ALIGN=MIDDLE  ALT=\"%285%2B2%29%285-4%29%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   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=7%3C+0 ALIGN=MIDDLE  ALT=\"7%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate and simplify the left side\r<BR>\n" );
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document.write( "Since the inequality is false, this means that the interval does <b>not</b> work. So this interval is <b>not</b> in our solution set and we can ignore it.\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "So the solution set is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|-2 < x < 4\right\}\">\r<BR>\n" );
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document.write( "So the solution in interval notation is:\r<BR>\n" );
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document.write( "<font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -2,4\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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