document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39207>Question 39207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality |x - 1/2| > or = 2/3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24659 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24659\">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%28x+-+%281%2F2%29%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+abs%28x+-+%281%2F2%29%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > means we have 2 possibilities since the |.| part is like a V-shape, ie 2 straight lines. Mathematically we have to solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+%281%2F2%29%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+%28x+-+%281%2F2%29%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%28x+-+%281%2F2%29%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+-%28x+-+%281%2F2%29%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+%281%2F2%29%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+%28x+-+%281%2F2%29%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+%283%2F6%29%29+%3E=+4%2F6+ ALIGN=MIDDLE  ALT=\"+%28x+-+%283%2F6%29%29+%3E=+4%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E=+4%2F6+%2B+3%2F6+ ALIGN=MIDDLE  ALT=\"+x+%3E=+4%2F6+%2B+3%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E=+7%2F6+ ALIGN=MIDDLE  ALT=\"+x+%3E=+7%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and now: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%28x+-+%281%2F2%29%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+-%28x+-+%281%2F2%29%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-x+%2B+%281%2F2%29+%3E=+2%2F3+ ALIGN=MIDDLE  ALT=\"+-x+%2B+%281%2F2%29+%3E=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-x+%2B+%283%2F6%29+%3E=+4%2F6+ ALIGN=MIDDLE  ALT=\"+-x+%2B+%283%2F6%29+%3E=+4%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-x+%3E=+4%2F6+-+3%2F6+ ALIGN=MIDDLE  ALT=\"+-x+%3E=+4%2F6+-+3%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-x+%3E=+1%2F6+ ALIGN=MIDDLE  ALT=\"+-x+%3E=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+-1%2F6+ ALIGN=MIDDLE  ALT=\"+x+%3C=+-1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the value of x needs to be \"less than or equal to\" (-1/6) OR \"greater than or equal to\" (7/6)\r<BR>\n" );
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document.write( "Graphically, we can show this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C-2%2C3%2C-2%2C3%2Cabs%28x+-+%281%2F2%29%29%2C+%282%2F3%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C-2%2C3%2C-2%2C3%2Cabs%28x+-+%281%2F2%29%29%2C+%282%2F3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where i have plotted both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+abs%28x+-+%281%2F2%29%29+ ALIGN=MIDDLE  ALT=\"+y+=+abs%28x+-+%281%2F2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Where they cross each other are the 2 answers i calculated\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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