document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230648>Question 230648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all x-y such that |x+y|=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170832 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=170832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> |x+y| = 1 means that:\r<BR>\n" );
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document.write( "If the expression (x+y) >= 0, then:\r<BR>\n" );
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document.write( "x + y = 1\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "x = 1-y\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "Let y = 5<BR>\n" );
document.write( "x = 1-5 = -4\r<BR>\n" );
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document.write( "|-4 + 5| = |1| = 1 which is true so this looks good.\r<BR>\n" );
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document.write( "We have so far:\r<BR>\n" );
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document.write( "x = 1-y when the expression (x+y) is greater than or equal to 0.\r<BR>\n" );
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document.write( "If the expression (x+y) < 0, then:\r<BR>\n" );
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document.write( "- (x+y) = 1\r<BR>\n" );
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document.write( "Multiply both sides of this by (-1) to get:\r<BR>\n" );
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document.write( "(x+y) = -1\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "x = -1 - y\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "Let y = 5\r<BR>\n" );
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document.write( "This means that x = -1 - 5 = -6\r<BR>\n" );
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document.write( "If x = -6 and y = 5, we get:\r<BR>\n" );
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document.write( "(x+y) = (-6 + 5) = -1 < 0\r<BR>\n" );
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document.write( "We also get:\r<BR>\n" );
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document.write( "|x + y| = |-6 + 5| = 1 which becomes |-1| = 1 which becomes 1 = 1 so this is good.\r<BR>\n" );
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document.write( "Your solution should be, if I understand the problem correctly:\r<BR>\n" );
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document.write( "x = 1-y<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = -1-y\r<BR>\n" );
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document.write( "Let's see how that holds up.\r<BR>\n" );
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document.write( "Let y be any number.\r<BR>\n" );
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document.write( "We'll try -5 and 5\r<BR>\n" );
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document.write( "When y = -5, x will be either:\r<BR>\n" );
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document.write( "1-(-5) = 6<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "-1-(-5) = 4\r<BR>\n" );
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document.write( "If x = 6 and y = -5, then |x+y| = |6-5| = |1| = 1 which is good.\r<BR>\n" );
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document.write( "If x = 4 and y = -5, then |x+y| = |4 -5| = |-1| = 1 which is good.\r<BR>\n" );
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document.write( "When y = 5, x with be either:\r<BR>\n" );
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document.write( "1 - 5 = -4<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "-1 - 5 = -6\r<BR>\n" );
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document.write( "If x = -5 and y = 5, then |x+y| = |-4 + 5| = |1| = 1 which is good.\r<BR>\n" );
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document.write( "If x = -6 and y = 5, then |x+y| = |-6 + 5| = |-1| = 1 which is good.\r<BR>\n" );
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document.write( "Your answer is:\r<BR>\n" );
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document.write( "x = 1-y<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = -1-y\r<BR>\n" );
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document.write( " </SPAN>\n" );
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