document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148536>Question 1148536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the sum of all the solutions of x = |2x-|60-2x||? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769888 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=769888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Find equivalent expressions for the given function<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-abs%2860-2x%29%29 ALIGN=MIDDLE  ALT=\"abs%282x-abs%2860-2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "for different ranges of values for x.<br><BR>\n" );
document.write( "Case 1: x>30<br><BR>\n" );
document.write( "When x>30, 2x>60, and (60-2x) is negative; that means<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2860-2x%29+=+2x-60 ALIGN=MIDDLE  ALT=\"abs%2860-2x%29+=+2x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-abs%2860-2x%29%29+=+abs%282x-%282x-60%29%29+=+abs%2860%29+=+60 ALIGN=MIDDLE  ALT=\"abs%282x-abs%2860-2x%29%29+=+abs%282x-%282x-60%29%29+=+abs%2860%29+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So on the interval x>30, the only solution to the given equation is x=60.<br><BR>\n" );
document.write( "Case 2: x<30<br><BR>\n" );
document.write( "When x<30, 2x<60, and (60-2x) is positive; that means<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2860-2x%29+=+60-2x ALIGN=MIDDLE  ALT=\"abs%2860-2x%29+=+60-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29 ALIGN=MIDDLE  ALT=\"abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%2860-4x%29 ALIGN=MIDDLE  ALT=\"abs%2860-4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive for x<15 and negative for x>15, so we need to break case 2 into two sub-cases.<br><BR>\n" );
document.write( "Case 2a: x<15<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29+=+60-4x ALIGN=MIDDLE  ALT=\"abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29+=+60-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So on the interval x<15, the solution to the given equation will be when<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+60-4x ALIGN=MIDDLE  ALT=\"x+=+60-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+60 ALIGN=MIDDLE  ALT=\"5x+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Case 2b: x>15 and x<30<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29+=+4x-60 ALIGN=MIDDLE  ALT=\"abs%282x-abs%2860-2x%29%29+=+abs%282x-%2860-2x%29%29+=+abs%2860-4x%29+=+4x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So on the interval (15,30), the solution to the given equation will be when<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4x-60 ALIGN=MIDDLE  ALT=\"x+=+4x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+=+3x ALIGN=MIDDLE  ALT=\"60+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: There are three solutions to the equation: x=12, x=20, and x=60.<br><BR>\n" );
document.write( "A graph....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C-10%2C90%2C-10%2C90%2Cabs%282x-abs%2860-2x%29%29%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C-10%2C90%2C-10%2C90%2Cabs%282x-abs%2860-2x%29%29%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );