document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050825>Question 1050825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The solution set of the equation |2x|=|10x| is given by: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666434 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=666434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe that the only solution to this equation is when x = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the basic definition of absolute value is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "|a| is equal to a when a is positive and is equal to -a when a is negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the absolute value of an expression will always be positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the expression is positive, the absolute value of the expression is equal to the expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the expression is negative, the absolute value of the expression is equal to -1 * the expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we start with |2x| = |10x|\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by definition |10x| = 10x if x is positive and is equal to -10x if x is negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "by definition |2x| = 2x if x is positive and is equal to -2x if x is negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 4 possibilities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = 10x \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = -10x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-2x = 10x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-2x = -10x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can reduce this to 2 possibilities, because 2 of the equations are equivalent to the other 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = -10x is equivalent to -2x = 10x because, if you multiply both sides of -2x = 10x by -1, you get 2x = -10x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "likewise, 2x = 10x is equivalent to -2x = -10x because, if you multiply both sides of -2x = -10x by -1, you get 2x = 10x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you therefore have 2 possibilities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = 10x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x = -10x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you solve for x in both equations, you will find that x = 0 is the only solution applicable to each of those equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "therefore, the only solution set possible for |2x| = |10x| is x = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you graph y = |2x| and y = |10x|, you will see that the only intersection of the lines created by those 2 equations is when x = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/100203.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );