document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090338>Question 1090338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality (x-2)^2(x+1)^3(x-5) <_0\r<BR>\n" );
document.write( "\n" );
document.write( "if you could please thoroughly explain it because I am completely lost on this one. I tried to distribute (not sure if we're even supposed to) the entire thing and got lost </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704865 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No, break up the number line into distinct regions using the critical values of the inequality (values that make the left hand side equal zero).<BR>\n" );
document.write( "So,<BR>\n" );
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;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "So then the four regions are:<BR>\n" );
document.write( "Region 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1 ALIGN=MIDDLE  ALT=\"x%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Region 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-1%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Region 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx%3C5 ALIGN=MIDDLE  ALT=\"2%3Cx%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Region 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E5 ALIGN=MIDDLE  ALT=\"x%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For each region, choose a value in the region (not an endpoint), test the inequality, determine if that point is part of the solution.<BR>\n" );
document.write( "Region 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-1 ALIGN=MIDDLE  ALT=\"x%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2-2%29%5E2%2A%28-2%2B1%29%5E3%2A%28-2-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%28-2-2%29%5E2%2A%28-2%2B1%29%5E3%2A%28-2-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%5E2%2A%28-1%29%5E3%2A%28-7%29%3C=0 ALIGN=MIDDLE  ALT=\"%28-4%29%5E2%2A%28-1%29%5E3%2A%28-7%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%29%2A%28-1%29%2A%28-7%29%3C=0 ALIGN=MIDDLE  ALT=\"%2816%29%2A%28-1%29%2A%28-7%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=112%3C=0 ALIGN=MIDDLE  ALT=\"112%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, not part of the solution.<BR>\n" );
document.write( "Region 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-1%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-2%29%5E2%2A%280%2B1%29%5E3%2A%280-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%280-2%29%5E2%2A%280%2B1%29%5E3%2A%280-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2A%281%29%2A%28-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%284%29%2A%281%29%2A%28-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%3C=0 ALIGN=MIDDLE  ALT=\"-5%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, part of the solution.<BR>\n" );
document.write( "Region 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx%3C5 ALIGN=MIDDLE  ALT=\"2%3Cx%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2%29%5E2%2A%283%2B1%29%5E3%2A%283-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%283-2%29%5E2%2A%283%2B1%29%5E3%2A%283-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2A%2864%29%2A%28-2%29%3C=0 ALIGN=MIDDLE  ALT=\"%281%29%2A%2864%29%2A%28-2%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128%3C=0 ALIGN=MIDDLE  ALT=\"-128%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, part of the solution.<BR>\n" );
document.write( "Region 4: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E5 ALIGN=MIDDLE  ALT=\"x%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2A%28x%2B1%29%5E3%2A%28x-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-2%29%5E2%2A%286%2B1%29%5E3%2A%286-5%29%3C=0 ALIGN=MIDDLE  ALT=\"%286-2%29%5E2%2A%286%2B1%29%5E3%2A%286-5%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%29%2A%28343%29%2A%281%29%3C=0 ALIGN=MIDDLE  ALT=\"%2816%29%2A%28343%29%2A%281%29%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5488%3C=0 ALIGN=MIDDLE  ALT=\"5488%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, not part of the solution.<BR>\n" );
document.write( "So then, the solution region is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-1%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" >U<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx%3C5 ALIGN=MIDDLE  ALT=\"2%3Cx%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The inequality also holds when <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;\" > because of the equal sign in the inequality so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C=x%3C=5 ALIGN=MIDDLE  ALT=\"-1%3C=x%3C=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=fer19.JPG\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );