document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148537>Question 1148537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the number of distinct solutions of the equation |x-|2x+1||=3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769890 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=769890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > when x = -1/2.  So consider two cases, one with x < -1/2 and the other with x > -1/2.<br><BR>\n" );
document.write( "Case 1: x < -1/2; 2x+1 < 0<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x%2B1%29+=+-2x-1 ALIGN=MIDDLE  ALT=\"abs%282x%2B1%29+=+-2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-abs%282x%2B1%29%29+=+abs%28x-%28-2x-1%29%29+=+abs%283x%2B1%29+=+-3x-1 ALIGN=MIDDLE  ALT=\"abs%28x-abs%282x%2B1%29%29+=+abs%28x-%28-2x-1%29%29+=+abs%283x%2B1%29+=+-3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The solution on the interval x < -1/2 is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-1+=+3 ALIGN=MIDDLE  ALT=\"-3x-1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+=+4 ALIGN=MIDDLE  ALT=\"-3x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4%2F3 ALIGN=MIDDLE  ALT=\"x+=+-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Case 2: x > -1/2; 2x+1 > 0<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x%2B1%29+=+2x%2B1 ALIGN=MIDDLE  ALT=\"abs%282x%2B1%29+=+2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-abs%282x%2B1%29%29+=+abs%28x-%282x%2B1%29%29+=+abs%28-x-1%29+=+x%2B1 ALIGN=MIDDLE  ALT=\"abs%28x-abs%282x%2B1%29%29+=+abs%28x-%282x%2B1%29%29+=+abs%28-x-1%29+=+x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The solution on the interval x > -1/2 is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1+=+3 ALIGN=MIDDLE  ALT=\"x%2B1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: There are two solutions to the equation: -4/3 and 2.<br><BR>\n" );
document.write( "A graph, showing the intersection of the two graphs at x=-4/3 and x=2....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C-3%2C3%2C-1%2C5%2Cabs%28x-abs%282x%2B1%29%29%2C3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C-3%2C3%2C-1%2C5%2Cabs%28x-abs%282x%2B1%29%29%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );