document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201220>Question 201220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me solve and graph the inequality and graph the solution.\r<BR>\n" );
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document.write( "-8x - 2 (greater than or equal to) - 7x - 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151416 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=151416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x-2%3E=-7x-12 ALIGN=MIDDLE  ALT=\"-8x-2%3E=-7x-12\"   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=-8x%3E=-7x-12%2B2 ALIGN=MIDDLE  ALT=\"-8x%3E=-7x-12%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%2B7x%3E=-12%2B2 ALIGN=MIDDLE  ALT=\"-8x%2B7x%3E=-12%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x ALIGN=MIDDLE  ALT=\"7x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E=-12%2B2 ALIGN=MIDDLE  ALT=\"-x%3E=-12%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E=-10 ALIGN=MIDDLE  ALT=\"-x%3E=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=%28-10%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x%3C=%28-10%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=10 ALIGN=MIDDLE  ALT=\"x%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=10 ALIGN=MIDDLE  ALT=\"x%3C=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the answer in interval notation is   <font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-\infty,10}\"><font size=\"8\">]</font>\r<BR>\n" );
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document.write( "Also, the answer in set-builder notation is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|x\le10\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set on a number line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C0%2C+20%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+0%2C+20%29%2C%0D%0A%0D%0A%0D%0Aarrow%2810%2C0%2C0%2C0%29%2C%0D%0Aarrow%2810%2C0.30%2C0%2C0.30%29%2C%0D%0Aarrow%2810%2C0.15%2C0%2C0.15%29%2C%0D%0Aarrow%2810%2C-0.15%2C0%2C-0.15%29%2C%0D%0Aarrow%2810%2C-0.30%2C0%2C-0.30%29%2C%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Acircle%2810%2C0%2C0.2%29%2C%0D%0Acircle%2810%2C0%2C0.15%29%2C%0D%0Acircle%2810%2C0%2C0.1%29%2C%0D%0Acircle%2810%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( "Note: there is a CLOSED circle at the endpoint. </SPAN>\n" );
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