document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196829>Question 196829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I came up with an incorrect answer for the following problem and I'm not sure why, can you assist me?\r<BR>\n" );
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document.write( "Solve the absolute value inequality. Express the solution using interval notation and graph the solution set.\r<BR>\n" );
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document.write( "abs(4x) > 6\r<BR>\n" );
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document.write( "thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147543 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=147543\">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=abs%284x%29%3E6 ALIGN=MIDDLE  ALT=\"abs%284x%29%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality\r<BR>\n" );
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document.write( "Break up the absolute value (remember, if you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29%3E+a ALIGN=MIDDLE  ALT=\"abs%28x%29%3E+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-a ALIGN=MIDDLE  ALT=\"x+%3C+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+a ALIGN=MIDDLE  ALT=\"x+%3E+a\"   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+-6 ALIGN=MIDDLE  ALT=\"4x+%3C+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%3E+6 ALIGN=MIDDLE  ALT=\"4x+%3E+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the absolute value inequality using the given rule\r<BR>\n" );
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document.write( "Now lets focus on the first inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%3C+-6 ALIGN=MIDDLE  ALT=\"4x+%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=4x%3C-6 ALIGN=MIDDLE  ALT=\"4x%3C-6\"   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=x%3C%28-6%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x%3C%28-6%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 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-3%2F2 ALIGN=MIDDLE  ALT=\"x%3C-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now lets focus on the second inequality  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%3E+6 ALIGN=MIDDLE  ALT=\"4x+%3E+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=4x%3E6 ALIGN=MIDDLE  ALT=\"4x%3E6\"   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=x%3E%286%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x%3E%286%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 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%3E3%2F2 ALIGN=MIDDLE  ALT=\"x%3E3%2F2\"   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\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-3%2F2 ALIGN=MIDDLE  ALT=\"x+%3C+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+3%2F2 ALIGN=MIDDLE  ALT=\"x+%3E+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which looks like this in interval notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,-\frac{3}{2}\right)\cup\left(\frac{3}{2},\infty\right)\">\r<BR>\n" );
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document.write( "if you wanted to graph the solution set, you would get\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%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-10%2C+10%29%2C%0D%0A%0D%0Ablue%28arrow%28-2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-2%2C-5%2C-10%2C-5%29%29%2C%0D%0Ablue%28arrow%282%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%282%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%282%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%282%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%282%2C-5%2C10%2C-5%29%29%2C%0D%0A%0D%0Acircle%28-1.5%2C-5.8%2C0.35%29%2C%0D%0Acircle%28-1.5%2C-5.8%2C0.4%29%2C%0D%0Acircle%28-1.5%2C-5.8%2C0.45%29%2C%0D%0A%0D%0A%0D%0Acircle%281.5%2C-5.8%2C0.35%29%2C%0D%0Acircle%281.5%2C-5.8%2C0.4%29%2C%0D%0Acircle%281.5%2C-5.8%2C0.45%29%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the solution set in blue and the excluded values represented by open circles </SPAN>\n" );
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