document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112831>Question 1112831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What do two equivalent expressions always have in common?\r<BR>\n" );
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document.write( "The same value<BR>\n" );
document.write( "The same variables <BR>\n" );
document.write( "The same constants<BR>\n" );
document.write( "Or both have an equal sign\r<BR>\n" );
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document.write( "I’m really not sure which it is, but I think it’s the same value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727845 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Yes.\r<BR>\n" );
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document.write( "Consider the other answers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ -\ b\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ b\"> have the same variables.  Equivalent only if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ =\ 0\">, in which case the two expressions would have the same value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ +\ 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\ +\ 2\">.  Equivalent ONLY if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ =\ b\">, in which case the two expressions would have the same value.\r<BR>\n" );
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document.write( "The \"value\" of an expression containing an equals sign is either \"true\" or \"false\".  The fact that two expressions each have an equals sign in them does not guarantee equivalence since one of the statements might be true and the other false.  For example, consider:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 5x\ +\ 6\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 1\">\r<BR>\n" );
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document.write( "If either of these statements is true, then the other one is not.  Actually, they could both be false which is a very loose form of equivalence, but certainly not equivalent in the context that I think you are working in.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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