document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917392>Question 917392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference of the aboslute value of two numbers is the same as the difference of the two numbers themselves. adding 1 to a numbers always increases its abosulte value. true or false, give a counterexample. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556643 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=556643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> definitions:<BR>\n" );
document.write( "abs(x) means absolute value of x.<BR>\n" );
document.write( "|x| means absolute value of x.<BR>\n" );
document.write( "abs(x) means |x|\r<BR>\n" );
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document.write( "in order for the statement to be true, it has to be true under all conditions.  if it's not true under all conditions, then it's false.\r<BR>\n" );
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document.write( "the difference of the absolute value of two number is not the same as the difference of the two numbers themselves.<BR>\n" );
document.write( "this is false because sometimes it's true and sometimes it's false.<BR>\n" );
document.write( "example where it's false.<BR>\n" );
document.write( "5 - 5 = 0<BR>\n" );
document.write( "abs(5) = 5<BR>\n" );
document.write( "abs(5) - abs(5) = 5 - 5 = 0<BR>\n" );
document.write( "it's false because the difference is the same (0 = 0).<BR>\n" );
document.write( "example where it's true.<BR>\n" );
document.write( "5 - (-5) = 5 + 5 = 10<BR>\n" );
document.write( "abs(5) = 5<BR>\n" );
document.write( "abs(-5) = 5<BR>\n" );
document.write( "abs(5) - abs(-5) = 5 - 5 = 0<BR>\n" );
document.write( "it's true because they're not the same (10 <> 0).\r<BR>\n" );
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document.write( "adding 1 to a number always increases its absolute value.<BR>\n" );
document.write( "this is false because sometimes it's true and sometimes it's false.<BR>\n" );
document.write( "example of where it's false.<BR>\n" );
document.write( "abs(-5) = 5<BR>\n" );
document.write( "abs(-5+1) = abs(4) = 4<BR>\n" );
document.write( "it's false because 4 is not greater than 5.<BR>\n" );
document.write( "example of where it's true.<BR>\n" );
document.write( "abs(5) = 5<BR>\n" );
document.write( "abs(5+1) = abs(6) = 6<BR>\n" );
document.write( "it's true because 6 is greater than 5.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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