document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110602>Question 110602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve and graph the solution set.<BR>\n" );
document.write( "3(x-4)>7x-9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80794 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=80794\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-4%29%3E7x-9 ALIGN=MIDDLE  ALT=\"3%28x-4%29%3E7x-9\"   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=3x-12%3E7x-9 ALIGN=MIDDLE  ALT=\"3x-12%3E7x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%3E7x-9%2B12 ALIGN=MIDDLE  ALT=\"3x%3E7x-9%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 12 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-7x%3E-9%2B12 ALIGN=MIDDLE  ALT=\"3x-7x%3E-9%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 7x 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%3E-9%2B12 ALIGN=MIDDLE  ALT=\"-4x%3E-9%2B12\"   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=-4x%3E3 ALIGN=MIDDLE  ALT=\"-4x%3E3\"   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%283%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"x%3C%283%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-3%2F4 ALIGN=MIDDLE  ALT=\"x%3C-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Answer:\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-3%2F4 ALIGN=MIDDLE  ALT=\"x%3C-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (which is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-0.75 ALIGN=MIDDLE  ALT=\"x%3C-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form)\r<BR>\n" );
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document.write( "Now let's graph the solution set\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-3%2F4 ALIGN=MIDDLE  ALT=\"x%3C-3%2F4\"   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-13%2C7%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-13%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now plot the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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-13%2C7%2C+-3%2F4%29 ALIGN=MIDDLE  ALT=\"number_line%28500%2C-13%2C7%2C+-3%2F4%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-3%2F4 ALIGN=MIDDLE  ALT=\"x%3C-3%2F4\"   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-3%2F4 ALIGN=MIDDLE  ALT=\"0%3C-3%2F4\"   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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the boundary. This means we shade everything to the left of the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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-13%2C7%2C-10%2C10%2C%0D%0Anumber_line%28500%2C-13%2C7%29%2C%0D%0Acircle%28-3%2F4%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-3%2F4%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-3%2F4%2C-5.8%2C0.45%29%2C%0D%0Ablue%28line%28-3%2F4%2C-5%2C-3%2F4-10%2C-5%29%29%2C%0D%0Ablue%28line%28-3%2F4%2C-6%2C-3%2F4-10%2C-6%29%29%2C%0D%0Ablue%28line%28-3%2F4%2C-7%2C-3%2F4-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-3%2F4%2C-5%2C-3%2F4-10.2%2C-5%29%29%2C%0D%0Ablue%28arrow%28-3%2F4%2C-5.5%2C-3%2F4-10.2%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-3%2F4%2C-6%2C-3%2F4-10.2%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-3%2F4 ALIGN=MIDDLE  ALT=\"x%3C-3%2F4\"   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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is an <font size=4><b>open</b></font> circle. This means the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is excluded from the solution set.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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