document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146781>Question 146781</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve and graph<BR>\n" );
document.write( "4x-9 less than equal to -8 or x-8 greater than equal to 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107193 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=107193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-9%3C=-8 ALIGN=MIDDLE  ALT=\"4x-9%3C=-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=4x-9%3C=-8 ALIGN=MIDDLE  ALT=\"4x-9%3C=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%3C=-8%2B9 ALIGN=MIDDLE  ALT=\"4x%3C=-8%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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=4x%3C=1 ALIGN=MIDDLE  ALT=\"4x%3C=1\"   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=%281%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x%3C=%281%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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;\" >. \r<BR>\n" );
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document.write( "Now let's solve the second inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8%3E=1 ALIGN=MIDDLE  ALT=\"x-8%3E=1\"   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=x-8%3E=1 ALIGN=MIDDLE  ALT=\"x-8%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1%2B8 ALIGN=MIDDLE  ALT=\"x%3E=1%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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=9 ALIGN=MIDDLE  ALT=\"x%3E=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\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=1%2F4 ALIGN=MIDDLE  ALT=\"x%3C=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <font size=\"4\"><b>or</b></font>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=9 ALIGN=MIDDLE  ALT=\"x%3E=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solution in interval notation is: <font size=\"8\">(</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-\infty,\frac{1}{4}}\"><font size=\"8\">]</font> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cup\"><font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{9,\infty}\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( "Also, the solution in set notation is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|x\le\frac{1}{4} \textrm{..or..} x\ge9\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C-4.75%2C+14%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-4.75%2C+14+%2C1%2F4%2C9%29%2C%0D%0A%0D%0Ablue%28arrow%281%2F4%2C0%2C-4.75%2C0%29%29%2C%0D%0Ablue%28arrow%281%2F4%2C0.30%2C-4.75%2C0.30%29%29%2C%0D%0Ablue%28arrow%281%2F4%2C0.15%2C-4.75%2C0.15%29%29%2C%0D%0Ablue%28arrow%281%2F4%2C-0.15%2C-4.75%2C-0.15%29%29%2C%0D%0Ablue%28arrow%281%2F4%2C-0.30%2C-4.75%2C-0.30%29%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%289%2C0%2C14%2C0%29%29%2C%0D%0Ablue%28arrow%289%2C0.30%2C14%2C0.30%29%29%2C%0D%0Ablue%28arrow%289%2C0.15%2C14%2C0.15%29%29%2C%0D%0Ablue%28arrow%289%2C-0.15%2C14%2C-0.15%29%29%2C%0D%0Ablue%28arrow%289%2C-0.30%2C14%2C-0.30%29%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note:\r<BR>\n" );
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document.write( "There is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F4 ALIGN=MIDDLE  ALT=\"x=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including that value from the solution set.\r<BR>\n" );
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document.write( "Also, there is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including that value from the solution set.<BR>\n" );
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