document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151739>Question 151739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you graph -3x < -6 or x + 5 < -2?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111540 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=111540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%3C-6 ALIGN=MIDDLE  ALT=\"-3x%3C-6\"   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=-3x%3C-6 ALIGN=MIDDLE  ALT=\"-3x%3C-6\"   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=x%3E%28-6%29%2F%28-3%29 ALIGN=MIDDLE  ALT=\"x%3E%28-6%29%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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%3E2 ALIGN=MIDDLE  ALT=\"x%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\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%2B5%3C-2 ALIGN=MIDDLE  ALT=\"x%2B5%3C-2\"   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%2B5%3C-2 ALIGN=MIDDLE  ALT=\"x%2B5%3C-2\"   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%3C-2-5 ALIGN=MIDDLE  ALT=\"x%3C-2-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-7 ALIGN=MIDDLE  ALT=\"x%3C-7\"   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%3E2 ALIGN=MIDDLE  ALT=\"x%3E2\"   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%3C-7 ALIGN=MIDDLE  ALT=\"x%3C-7\"   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,-7}\"><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{2,\infty}\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( "So the solution in set notation is: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|x<-7 \textrm{..or..} x>2\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-12%2C+7%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-12%2C+7+%29%2C%0D%0A%0D%0A%0D%0Acircle%28-7%2C0%2C0.25%29%2C%0D%0Acircle%28-7%2C0%2C0.20%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%28-7%2C0%2C-12%2C0%29%29%2C%0D%0Ablue%28arrow%28-7%2C0.30%2C-12%2C0.30%29%29%2C%0D%0Ablue%28arrow%28-7%2C0.15%2C-12%2C0.15%29%29%2C%0D%0Ablue%28arrow%28-7%2C-0.15%2C-12%2C-0.15%29%29%2C%0D%0Ablue%28arrow%28-7%2C-0.30%2C-12%2C-0.30%29%29%2C%0D%0A%0D%0A%0D%0A%0D%0Acircle%282%2C0%2C0.25%29%2C%0D%0Acircle%282%2C0%2C0.20%29%2C%0D%0A%0D%0A%0D%0Ablue%28arrow%282%2C0%2C7%2C0%29%29%2C%0D%0Ablue%28arrow%282%2C0.30%2C7%2C0.30%29%29%2C%0D%0Ablue%28arrow%282%2C0.15%2C7%2C0.15%29%29%2C%0D%0Ablue%28arrow%282%2C-0.15%2C7%2C-0.15%29%29%2C%0D%0Ablue%28arrow%282%2C-0.30%2C7%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 an <b>open</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding that value from the solution set.\r<BR>\n" );
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document.write( "Also, there is an <b>open</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding that value from the solution set.<BR>\n" );
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