document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115227>Question 115227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3/5X_<-54\r<BR>\n" );
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document.write( "-1/3X<-27\r<BR>\n" );
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document.write( "please and sooooo many thank yous! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83815 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=83815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x%3C=-54 ALIGN=MIDDLE  ALT=\"%283%2F5%29x%3C=-54\"   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%29%28%283%2F5%29x%29=%285%29%28-54%29 ALIGN=MIDDLE  ALT=\"%285%29%28%283%2F5%29x%29=%285%29%28-54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 5. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-270 ALIGN=MIDDLE  ALT=\"3x=-270\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=%28-270%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x%3C=%28-270%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-90 ALIGN=MIDDLE  ALT=\"x%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-90 ALIGN=MIDDLE  ALT=\"x%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's graph the solution set\r<BR>\n" );
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document.write( "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%3C=-90 ALIGN=MIDDLE  ALT=\"x%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set up a number line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28500%2C-100%2C-80%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-100%2C-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now plot the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-90 ALIGN=MIDDLE  ALT=\"x=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the number line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28500%2C-100%2C-80%2C+-90%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-100%2C-80%2C+-90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now pick any test point you want, I'm going to choose x=0, and test the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-90 ALIGN=MIDDLE  ALT=\"x%3C=-90\"   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=0%3C=-90 ALIGN=MIDDLE  ALT=\"0%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "Since this inequality is <font size=4><b>not</b></font> true, we simply shade the entire portion that does <font size=4><b>not</b></font> contain the point x=0 using the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-90 ALIGN=MIDDLE  ALT=\"x=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the boundary. This means we shade everything to the left of the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-90 ALIGN=MIDDLE  ALT=\"x=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C-100%2C-80%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-100%2C-80%2C+-90%29%2C%0D%0Ablue%28line%28-90%2C-5%2C-90-10%2C-5%29%29%2C%0D%0Ablue%28line%28-90%2C-6%2C-90-10%2C-6%29%29%2C%0D%0Ablue%28line%28-90%2C-7%2C-90-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-90%2C-5%2C-90-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%28-90%2C-5.5%2C-90-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-90%2C-6%2C-90-10.2%2C-6%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-90 ALIGN=MIDDLE  ALT=\"x%3C=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in blue\r<BR>\n" );
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document.write( "note: at the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-90 ALIGN=MIDDLE  ALT=\"x=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is an <font size=4><b>closed</b></font> circle. This means the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-90 ALIGN=MIDDLE  ALT=\"x=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > is included from the solution set.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29x%3C-27 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29x%3C-27\"   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=%283%29%28%28-1%2F3%29x%29=%283%29%28-27%29 ALIGN=MIDDLE  ALT=\"%283%29%28%28-1%2F3%29x%29=%283%29%28-27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x=-81 ALIGN=MIDDLE  ALT=\"-1x=-81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E%28-81%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x%3E%28-81%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E81 ALIGN=MIDDLE  ALT=\"x%3E81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E81 ALIGN=MIDDLE  ALT=\"x%3E81\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's graph the solution set\r<BR>\n" );
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document.write( "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%3E81 ALIGN=MIDDLE  ALT=\"x%3E81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set up a number line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28500%2C71%2C91%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C71%2C91%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now plot the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=81 ALIGN=MIDDLE  ALT=\"x=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the number line\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28500%2C71%2C91%2C+81%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C71%2C91%2C+81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now pick any test point you want, I'm going to choose x=0, and test the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E81 ALIGN=MIDDLE  ALT=\"x%3E81\"   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=0%3E81 ALIGN=MIDDLE  ALT=\"0%3E81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" >\r<BR>\n" );
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document.write( "Since this inequality is <font size=4><b>not</b></font> true, we simply shade the entire portion that does <font size=4><b>not</b></font> contain the point x=0 using the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=81 ALIGN=MIDDLE  ALT=\"x=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the boundary. This means we shade everything to the right of the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=81 ALIGN=MIDDLE  ALT=\"x=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C71%2C91%2C-10%2C10%2C%0D%0Anumber_line%28500%2C71%2C91%29%2C%0D%0Acircle%2881%2C-5.8%2C0.35%29%2C%0D%0Acircle%2881%2C-5.8%2C0.4%29%2C%0D%0Acircle%2881%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%2881%2C-5%2C81%2B10%2C-5%29%29%2C%0D%0Ablue%28line%2881%2C-6%2C81%2B10%2C-6%29%29%2C%0D%0Ablue%28line%2881%2C-7%2C81%2B10%2C-7%29%29%2C%0D%0Ablue%28arrow%2881%2C-5%2C81%2B10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%2881%2C-5.5%2C81%2B10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%2881%2C-6%2C81%2B10.2%2C-6%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E81 ALIGN=MIDDLE  ALT=\"x%3E81\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the shaded region in blue\r<BR>\n" );
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document.write( "note: at the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=81 ALIGN=MIDDLE  ALT=\"x=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is an <font size=4><b>open</b></font> circle. This means the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=81 ALIGN=MIDDLE  ALT=\"x=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > is excluded from the solution set.\r<BR>\n" );
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