document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207433>Question 207433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> set notation and graph it:-2(3+x)<4x+4<8x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156853 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=156853\">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=-2%283%2Bx%29%3C4x%2B4%3C8x ALIGN=MIDDLE  ALT=\"-2%283%2Bx%29%3C4x%2B4%3C8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given compound inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6-2x%3C4x%2B4%3C8x ALIGN=MIDDLE  ALT=\"-6-2x%3C4x%2B4%3C8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Break up the compound inequality to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6-2x%3C4x%2B4 ALIGN=MIDDLE  ALT=\"-6-2x%3C4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B4%3C8x ALIGN=MIDDLE  ALT=\"4x%2B4%3C8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So let's solve the first inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6-2x%3C4x%2B4 ALIGN=MIDDLE  ALT=\"-6-2x%3C4x%2B4\"   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=-6-2x%3C4x%2B4 ALIGN=MIDDLE  ALT=\"-6-2x%3C4x%2B4\"   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=-2x%3C4x%2B4%2B6 ALIGN=MIDDLE  ALT=\"-2x%3C4x%2B4%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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=-2x-4x%3C4%2B6 ALIGN=MIDDLE  ALT=\"-2x-4x%3C4%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   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=-6x%3C4%2B6 ALIGN=MIDDLE  ALT=\"-6x%3C4%2B6\"   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=-6x%3C10 ALIGN=MIDDLE  ALT=\"-6x%3C10\"   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%3E%2810%29%2F%28-6%29 ALIGN=MIDDLE  ALT=\"x%3E%2810%29%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   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%3E-5%2F3 ALIGN=MIDDLE  ALT=\"x%3E-5%2F3\"   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%2B4%3C8x ALIGN=MIDDLE  ALT=\"4x%2B4%3C8x\"   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%2B4%3C8x ALIGN=MIDDLE  ALT=\"4x%2B4%3C8x\"   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=4x%3C8x-4 ALIGN=MIDDLE  ALT=\"4x%3C8x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=4x-8x%3C-4 ALIGN=MIDDLE  ALT=\"4x-8x%3C-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x ALIGN=MIDDLE  ALT=\"8x\"   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=-4x%3C-4 ALIGN=MIDDLE  ALT=\"-4x%3C-4\"   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%28-4%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x%3E%28-4%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%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "If we combine the results <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E-5%2F3 ALIGN=MIDDLE  ALT=\"x%3E-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <b>and</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: we're essentially performing a set intersection between the two results.\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%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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\|x>1\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( " </SPAN>\n" );
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