document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84531>Question 84531</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve:<BR>\n" );
document.write( "The absolute value of n-6 = the absolute value of 1-n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60898 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=60898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28n-6%29+=+abs%281-n%29 ALIGN=MIDDLE  ALT=\"abs%28n-6%29+=+abs%281-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A methodical way of solving this equation involves understanding that each of the quantities <BR>\n" );
document.write( "in the absolute value signs can be either plus or minus without changing the equation<BR>\n" );
document.write( "... and this is due to the absolute value signs which change negative quantities to <BR>\n" );
document.write( "positive quantities.<BR>\n" );
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document.write( "Therefore, you have 4 possibilities:<BR>\n" );
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document.write( "+(n - 6) = +(1 - n) and<BR>\n" );
document.write( "-(n - 6) = +(1 - n) and<BR>\n" );
document.write( "+(n - 6) = -(1 - n) and finally<BR>\n" );
document.write( "-(n - 6) = -(1 - n)<BR>\n" );
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document.write( "Solve each of these four possible cases.<BR>\n" );
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document.write( "Case I. <BR>\n" );
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document.write( "+(n - 6) = +(1 - n) which is<BR>\n" );
document.write( "n - 6 = 1 - n and add n to both sides to get<BR>\n" );
document.write( "2n - 6 = 1 and add +6 to both sides to get<BR>\n" );
document.write( "2n = 7 and divide by 2 to find that<BR>\n" );
document.write( "n = 7/2<BR>\n" );
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document.write( "Case II<BR>\n" );
document.write( "-(n - 6) = +(1 - n) and the minus sign changes the left side <BR>\n" );
document.write( "-n + 6 = 1 - n  now add n to both sides and you get<BR>\n" );
document.write( "+6 = +1 ... this case does not lead to a good solution for n<BR>\n" );
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document.write( "Case III<BR>\n" );
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document.write( "+(n - 6) = -(1 - n) and the minus sign changes the right side<BR>\n" );
document.write( "n - 6 = -1 + n  subtract n from both sides and you get<BR>\n" );
document.write( "-6 = -1 ... this case also does not lead to a good solution for n<BR>\n" );
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document.write( "Case IV<BR>\n" );
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document.write( "-(n - 6) = -(1 - n) and the minus signs on both sides change this to<BR>\n" );
document.write( "-n + 6 = -1 + n  subtract n from both sides and you get<BR>\n" );
document.write( "-2n + 6 = -1  subtract 6 from both sides and you get<BR>\n" );
document.write( "-2n = -7  divide both sides by -2 and the answer becomes<BR>\n" );
document.write( "n = -7/-2 = 7/2 This is the same answer as Case I<BR>\n" );
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document.write( "So the answer to the problem is n = +7/2. Let's check that by replacing n by 7/2 in the<BR>\n" );
document.write( "equation originally given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28n-6%29+=+abs%281-n%29 ALIGN=MIDDLE  ALT=\"abs%28n-6%29+=+abs%281-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 7/2 for n and this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%287%2F2+-+6%29+=+abs%281+-+7%2F2%29 ALIGN=MIDDLE  ALT=\"abs%287%2F2+-+6%29+=+abs%281+-+7%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Make each of the terms inside the absolute value signs have a common denominator of 2:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%287%2F2+-+12%2F2%29+=+abs%282%2F2+-+7%2F2%29 ALIGN=MIDDLE  ALT=\"abs%287%2F2+-+12%2F2%29+=+abs%282%2F2+-+7%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now combine the terms inside the absolute value signs and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-5%2F2%29+=+abs%28-5%2F2%29 ALIGN=MIDDLE  ALT=\"abs%28-5%2F2%29+=+abs%28-5%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Both sides of this equation are the same, so we can say that n = 7/2 is a solution<BR>\n" );
document.write( "to the equation.<BR>\n" );
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document.write( "Hope this helps you understand absolute values a little more. </SPAN>\n" );
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