document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93529>Question 93529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you work these problems? I have no Idea where to start! Help!\r<BR>\n" );
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document.write( "Solve and graph the solution:\r<BR>\n" );
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document.write( "-12 is greater than or equal to 24x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68111 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=68111\">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=-12%3E=24x ALIGN=MIDDLE  ALT=\"-12%3E=24x\"   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=24x%3C=-12 ALIGN=MIDDLE  ALT=\"24x%3C=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the sides so the variable is 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%3C=%28-12%29%2F%2824%29 ALIGN=MIDDLE  ALT=\"x%3C=%28-12%29%2F%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 24 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=-1+%2F+2 ALIGN=MIDDLE  ALT=\"x%3C=-1+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\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+%2F+2 ALIGN=MIDDLE  ALT=\"x%3C=-1+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form\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=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   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-10.5%2C9.5%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-10.5%2C9.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now plot the point x=-0.5 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-10.5%2C9.5%2C+-0.5%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-10.5%2C9.5%2C+-0.5%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=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   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=-0.5 ALIGN=MIDDLE  ALT=\"0%3C=-0.5\"   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 x=-0.5 as the boundary. This means we shade everything to the left of the point x=-0.5 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-10.5%2C9.5%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-10.5%2C9.5%2C+-0.5%29%2C%0D%0Ablue%28line%28-0.5%2C-5%2C-0.5-10%2C-5%29%29%2C%0D%0Ablue%28line%28-0.5%2C-6%2C-0.5-10%2C-6%29%29%2C%0D%0Ablue%28line%28-0.5%2C-7%2C-0.5-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.5%2C-5%2C-0.5-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.5%2C-5.5%2C-0.5-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.5%2C-6%2C-0.5-10.2%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=-0.5 ALIGN=MIDDLE  ALT=\"x%3C=-0.5\"   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 x=-0.5, there is an <b>closed</b> circle. This means the point x=-0.5 is included from the solution set.\r<BR>\n" );
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