document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117754>Question 117754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality and graph the solution.\r<BR>\n" );
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document.write( "y - 3 > or equal to 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85720 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=85720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3%3E=5 ALIGN=MIDDLE  ALT=\"y-3%3E=5\"   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=y%3E=5%2B3 ALIGN=MIDDLE  ALT=\"y%3E=5%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 3 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\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=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   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=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   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-2%2C18%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-2%2C18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > note: just replace the x with the variable you are working with\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=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   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-2%2C18%2C+8%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-2%2C18%2C+8%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 y=0, and test the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   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%3E=8 ALIGN=MIDDLE  ALT=\"0%3E=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=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 y=0 using the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   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=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   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-2%2C18%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-2%2C18%2C+8%29%2C%0D%0Ablue%28line%288%2C-5%2C8%2B10%2C-5%29%29%2C%0D%0Ablue%28line%288%2C-6%2C8%2B10%2C-6%29%29%2C%0D%0Ablue%28line%288%2C-7%2C8%2B10%2C-7%29%29%2C%0D%0Ablue%28arrow%288%2C-5%2C8%2B10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%288%2C-5.5%2C8%2B10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%288%2C-6%2C8%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=y%3E=8 ALIGN=MIDDLE  ALT=\"y%3E=8\"   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=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   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=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is included from the solution set.\r<BR>\n" );
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