document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151736>Question 151736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you graph x + 5 > 2x + 1 and -4x < -8? <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 #111543 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=111543\">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=x%2B5%3E2x%2B1 ALIGN=MIDDLE  ALT=\"x%2B5%3E2x%2B1\"   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%3E2x%2B1 ALIGN=MIDDLE  ALT=\"x%2B5%3E2x%2B1\"   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%3E2x%2B1-5 ALIGN=MIDDLE  ALT=\"x%3E2x%2B1-5\"   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-2x%3E1-5 ALIGN=MIDDLE  ALT=\"x-2x%3E1-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   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%3E1-5 ALIGN=MIDDLE  ALT=\"-x%3E1-5\"   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-4 ALIGN=MIDDLE  ALT=\"-x%3E-4\"   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%28-4%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"x%3C%28-4%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%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   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=-4x%3C-8 ALIGN=MIDDLE  ALT=\"-4x%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%3C-8 ALIGN=MIDDLE  ALT=\"-4x%3C-8\"   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%28-8%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x%3E%28-8%29%2F%28-4%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;\" >. 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( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <font size=\"4\"><b>and</b></font>  <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;\" >\r<BR>\n" );
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document.write( "This answer combines to the compound inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx%3C4 ALIGN=MIDDLE  ALT=\"2%3Cx%3C4\"   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{2,4}\"><font size=\"8\">)</font>\r<BR>\n" );
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document.write( "So the answer in set-builder notation is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\|2 < x < 4\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-3%2C+9%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-3%2C+9+%29%2C%0D%0A%0D%0Ablue%28line%282%2C0%2C4%2C0%29%29%2C%0D%0Ablue%28line%282%2C0.30%2C4%2C0.30%29%29%2C%0D%0Ablue%28line%282%2C0.15%2C4%2C0.15%29%29%2C%0D%0Ablue%28line%282%2C-0.15%2C4%2C-0.15%29%29%2C%0D%0Ablue%28line%282%2C-0.30%2C4%2C-0.30%29%29%2C%0D%0Acircle%282%2C0%2C0.25%29%2Ccircle%282%2C0%2C0.20%29%2C%0D%0Acircle%284%2C0%2C0.25%29%2C%0D%0Acircle%284%2C0%2C0.20%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the solution set\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=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding this 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=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding this value from the solution set. </SPAN>\n" );
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