document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135438>Question 135438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and give answer in interval notation\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 #99242 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=99242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2-8x+12\le0\">  Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-2)(x-6)\le0\">  Factor the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-2)(x-6)=0\">  Set the left side equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=2  \textrm{ or }   x=6  \"> Solve for x in each case\r<BR>\n" );
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document.write( "So this means that the critical values are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=2  \textrm{ or }   x=6  \">\r<BR>\n" );
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document.write( "Now plot the critical values on a number line\r<BR>\n" );
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document.write( "So let's evaluate a point that is to the left of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=2 \"> (which is the left most endpoint). Let's evaluate the value <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( "  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-2)(x-6)\le0\">  Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (1-2)(1-6)\le0\">  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/rendertex.cgi?\LARGE 5\le 0\">  Evaluate and simplify\r<BR>\n" );
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document.write( " Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 5\le 0\"> is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.\r<BR>\n" );
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document.write( "Now let's test a point that is in between the critical values <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=2 \"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=6 \">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-2)(x-6)\le0\">  Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (4-2)(4-6)\le0\">  Plug in <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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -4\le 0\">  Evaluate and simplify\r<BR>\n" );
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document.write( "So the graph now looks like \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-4%2C+16%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-4%2C+16%29%2C%0D%0A%0D%0A%0D%0Aline%282%2C0%2C6%2C0%29%2C%0D%0Aline%282%2C0.3%2C6%2C0.3%29%2C%0D%0Aline%282%2C0.15%2C6%2C0.15%29%2C%0D%0Aline%282%2C-0.15%2C6%2C-0.15%29%2C%0D%0Aline%282%2C-0.3%2C6%2C-0.3%29%2C%0D%0A%0D%0Acircle%286%2C0%2C0.2%29%2C%0D%0Acircle%286%2C0%2C0.15%29%2C%0D%0Acircle%286%2C0%2C0.1%29%2C%0D%0Acircle%286%2C0%2C0.2-0.02%29%2C%0D%0A%0D%0Acircle%282%2C0%2C0.2%29%2C%0D%0Acircle%282%2C0%2C0.15%29%2C%0D%0Acircle%282%2C0%2C0.1%29%2C%0D%0Acircle%282%2C0%2C0.2-0.02%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -4\le 0\"> is true, this means that one part of the solution in interval notation is <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2,6\"><font size=\"8\">]</font>\r<BR>\n" );
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document.write( "So let's evaluate a point that is to the right of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  x=6 \"> (which is the right most endpoint). Let's evaluate the value <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( "  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-2)(x-6)\le0\">  Start with the given inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (7-2)(7-6)\le0\">  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/rendertex.cgi?\LARGE 5\le 0\">  Evaluate and simplify\r<BR>\n" );
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document.write( " Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 5\le 0\"> is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.\r<BR>\n" );
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document.write( "Answer:\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 2,6\"><font size=\"8\">]</font> </SPAN>\n" );
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