document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137593>Question 137593</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0536220794/algebrahomeworkh>Introductory and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Problem: Solve polynomial inequality and graph the solution set on a real number line.\r<BR>\n" );
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document.write( "(x+1)(x+2)(x+3)>=0\r<BR>\n" );
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document.write( "I have set each of the terms to equal 0.<BR>\n" );
document.write( "x+1=0   x+2=0   x+3=0<BR>\n" );
document.write( "x=-1    x=-2    x=-3\r<BR>\n" );
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document.write( "Then I placed these three numbers on a number line as boundary points.\r<BR>\n" );
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document.write( "I used the following test points:<BR>\n" );
document.write( "-1.5 which was >=0 (true)<BR>\n" );
document.write( "-2.5 which was not >=0 (false)<BR>\n" );
document.write( "-4 which was not >=0 (false)<BR>\n" );
document.write( "0 which was >=0 (true)\r<BR>\n" );
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document.write( "I am confused on how to plot this on the number line and write the solution set in set builder notation. I think that I would use [ at -1 and go right, but I am not clear on whether the next point would be set at -2 or -3.\r<BR>\n" );
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document.write( "I would have [-1, infinity) and ?<BR>\n" );
document.write( "{xIx>=-1 and ?}\r<BR>\n" );
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document.write( "Can you help me finish solving this problem. Thank you.\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 #100674 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=100674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your process is right on, but your arithmetic is faulty when you do the tests:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.5 ALIGN=MIDDLE  ALT=\"-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.5%2B1%29%28-1.5%2B2%29%28-1.5%2B3%29=%28-.5%29%28.5%29%281.5%29%3C0 ALIGN=MIDDLE  ALT=\"%28-1.5%2B1%29%28-1.5%2B2%29%28-1.5%2B3%29=%28-.5%29%28.5%29%281.5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (minus times plus times plus is minus), so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.5 ALIGN=MIDDLE  ALT=\"-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces a false result.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.5 ALIGN=MIDDLE  ALT=\"-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces a true result (minus times minus times plus is plus)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces a false result (minus times minus times minus is minus)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > produces a true result -- this one you got right.\r<BR>\n" );
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document.write( "So, anything smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is false,\r<BR>\n" );
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document.write( "Anything between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is true, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because of the 'or equal to' part of the original inequality.\r<BR>\n" );
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document.write( "Anything 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=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is false,\r<BR>\n" );
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document.write( "And finally, anything larger than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is true.\r<BR>\n" );
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document.write( "Hence your interval is <big><b>[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >] U [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)</b></big>\r<BR>\n" );
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document.write( "The big 'U' stands for 'union' or the set of all elements that are in either or both sets.\r<BR>\n" );
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document.write( "A graphical illustration of the situation can be found by multiplying the the three binomials together to get the cubic polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B6x%5E2%2B11x%2B6 ALIGN=MIDDLE  ALT=\"x%5E3%2B6x%5E2%2B11x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B6x%5E2%2B11x%2B6 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B6x%5E2%2B11x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The ordered pairs corresponding to those parts of the graph that are either on (equal to) or above (greater than) the x-axis are the solution set of the original inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28600%2C600%2C-5%2C5%2C-5%2C5%2Cx%5E3%2B6x%5E2%2B11x%2B6%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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