document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90877>Question 90877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please please help me figure this out! I am tearing out my hair over this problem:<BR>\n" );
document.write( "x/x-3<=-8/x-6   I need to solve and state the solution set. Thank you !!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65937 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=65937\">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%2F%28x-3%29%3C=-8%2F%28x-6%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-3%29%3C=-8%2F%28x-6%29\"   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=cross%28%28x-3%29%29%28x-6%29%28x%2Fcross%28%28x-3%29%29%29%3C=%28x-3%29cross%28%28x-6%29%29%28-8%2Fcross%28%28x-6%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-6%29%3C=-8%28x-3%29 ALIGN=MIDDLE  ALT=\"x%28x-6%29%3C=-8%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%3C=-8x%2B24 ALIGN=MIDDLE  ALT=\"x%5E2-6x%3C=-8x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-24%3C=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-24%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to one side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%28x-4%29%3C=0 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%28x-4%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "So our zeros are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   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( "This means we can plug in values near <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   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;\" > to find out if they produce y values that are less than zero:\r<BR>\n" );
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document.write( "Now lets test everything from negative infinity to x=-6\r<BR>\n" );
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document.write( "Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (any point less than x=-6 will work)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29=%28-7%29%5E2%2B2%28-7%29-24 ALIGN=MIDDLE  ALT=\"f%28-7%29=%28-7%29%5E2%2B2%28-7%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   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=f%28-7%29=%2849%29%2B2%28-7%29-24 ALIGN=MIDDLE  ALT=\"f%28-7%29=%2849%29%2B2%28-7%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise -7 to the second power to get 49\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29=%2849%29%2B-14-24 ALIGN=MIDDLE  ALT=\"f%28-7%29=%2849%29%2B-14-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by -7 to get -14\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-7%29=11 ALIGN=MIDDLE  ALT=\"f%28-7%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So x=-7 produces a y value greater than zero\r<BR>\n" );
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document.write( "So everything less than x=-6 will produce a y value greater than zero. So lets ignore this range\r<BR>\n" );
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document.write( "Now lets test everything from x=4 to infinity\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29 ALIGN=MIDDLE  ALT=\"f%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (any point greater than x=4 will work)\r<BR>\n" );
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document.write( "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=f%28x%29=x%5E2%2B2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=%285%29%5E2%2B2%285%29-24 ALIGN=MIDDLE  ALT=\"f%285%29=%285%29%5E2%2B2%285%29-24\"   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=f%285%29=%2825%29%2B2%285%29-24 ALIGN=MIDDLE  ALT=\"f%285%29=%2825%29%2B2%285%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise 5 to the second power to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=%2825%29%2B10-24 ALIGN=MIDDLE  ALT=\"f%285%29=%2825%29%2B10-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by 5 to get 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29=11 ALIGN=MIDDLE  ALT=\"f%285%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So everything greater than x=4 will produce a y value greater than zero. So lets ignore this range.\r<BR>\n" );
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document.write( "Now lets test everything from x=-6 to x=4\r<BR>\n" );
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document.write( "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;\" > (any point in between x=-6 and x=4 will work)\r<BR>\n" );
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document.write( "Lets evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29 ALIGN=MIDDLE  ALT=\"f%28-5%29\"   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=f%28x%29=x%5E2%2B2x-24 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29=%28-5%29%5E2%2B2%28-5%29-24 ALIGN=MIDDLE  ALT=\"f%28-5%29=%28-5%29%5E2%2B2%28-5%29-24\"   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=f%28-5%29=%2825%29%2B2%28-5%29-24 ALIGN=MIDDLE  ALT=\"f%28-5%29=%2825%29%2B2%28-5%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise -5 to the second power to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29=%2825%29%2B-10-24 ALIGN=MIDDLE  ALT=\"f%28-5%29=%2825%29%2B-10-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by -5 to get -10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29=-9 ALIGN=MIDDLE  ALT=\"f%28-5%29=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "So everything from x=-6 to x=4 will produce a y value less than zero\r<BR>\n" );
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document.write( "So the solution set is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3C=x%3C=4 ALIGN=MIDDLE  ALT=\"-6%3C=x%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which looks like this in interval notation\r<BR>\n" );
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document.write( "If we graph  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B2x-24 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B2x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see the range that is below y=0\r<BR>\n" );
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