document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933499>Question 933499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with absolute value in inequalities. <BR>\n" );
document.write( "What does it mean?<BR>\n" );
document.write( "The difference between 9 and 3 times the distance between x and -5 is greater than 6. <BR>\n" );
document.write( "I did try to to this. Here's what I think. 9-3|x-5|>6 only question. Is it supposed to be x-5 or x+5? And then i got the answer : -6>x>-4. Your help is greatly appreciated.. As i showed you here I did try but did not get the answer. Also tell me the definition of absolute value and how it is used in word problems if you would not mind. <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 #566835 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=566835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>The difference between 9 and 3 times the distance between x and -5 is greater than 6. </i>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-3%2Aabs%28x-%28-5%29%29%3E6 ALIGN=MIDDLE  ALT=\"9-3%2Aabs%28x-%28-5%29%29%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-3%2Aabs%28x%2B5%29%3E6 ALIGN=MIDDLE  ALT=\"9-3%2Aabs%28x%2B5%29%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Continue simplifying.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Aabs%28x%2B5%29%3E6-9 ALIGN=MIDDLE  ALT=\"-3%2Aabs%28x%2B5%29%3E6-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Aabs%28x%2B5%29%3E-3 ALIGN=MIDDLE  ALT=\"-3%2Aabs%28x%2B5%29%3E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides by a negative quantity will reverse the inequality direction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29%28-3%2Aabs%28x%2B5%29%29%3C%28-1%2F3%29%28-3%29 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29%28-3%2Aabs%28x%2B5%29%29%3C%28-1%2F3%29%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28abs%28x%2B5%29%3C1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28abs%28x%2B5%29%3C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x+5 could be negative or non-negative.  Solve for each case.\r<BR>\n" );
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document.write( "Non-negative,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%3C1 ALIGN=MIDDLE  ALT=\"x%2B5%3C1\"   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-4 ALIGN=MIDDLE  ALT=\"x%3C-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If negative,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-5%3C1 ALIGN=MIDDLE  ALT=\"-x-5%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%3E-1 ALIGN=MIDDLE  ALT=\"x%2B5%3E-1\"   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-1-5 ALIGN=MIDDLE  ALT=\"x%3E-1-5\"   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-6 ALIGN=MIDDLE  ALT=\"x%3E-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Put those two results together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-6%3Cx%3C-4%29 ALIGN=MIDDLE  ALT=\"highlight%28-6%3Cx%3C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The meaning of absolute value is how far from 0 on the number line.  For more detailed explanations and study, use your textbook.  Absolute Value is always a POSITIVE quantity. </SPAN>\n" );
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