document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193343>Question 1193343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a ∥ b ∥ c and B is the midpoint of AC.<BR>\n" );
document.write( "AB = 2x + 5, BC = x + 7, and DE = 3x + 6.<BR>\n" );
document.write( "x =<BR>\n" );
document.write( "Find the length of<BR>\n" );
document.write( "DE.<BR>\n" );
document.write( "DE =<BR>\n" );
document.write( "Because a ∥ b ∥ c and B is the midpoint of<BR>\n" );
document.write( "AC,E is the midpoint of<BR>\n" );
document.write( "DF and EF =<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find the length of<BR>\n" );
document.write( "EF. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848616 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's break down the problem step by step.\r<BR>\n" );
document.write( "\n" );
document.write( "**1. Find the value of x:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Since B is the midpoint of AC, AB = BC.<BR>\n" );
document.write( "* Therefore, 2x + 5 = x + 7<BR>\n" );
document.write( "* Solving for x, we get: x = 2\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Find the length of DE:**\r<BR>\n" );
document.write( "\n" );
document.write( "* DE = 3x + 6 <BR>\n" );
document.write( "* Substitute the value of x: DE = 3(2) + 6 <BR>\n" );
document.write( "* DE = 12\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Determine EF:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Given: a ∥ b ∥ c (lines a, b, and c are parallel) <BR>\n" );
document.write( "* Since B is the midpoint of AC and lines are parallel, E must be the midpoint of DF. <BR>\n" );
document.write( "* This is a property of parallel lines: Lines intersecting parallel lines create proportional segments.\r<BR>\n" );
document.write( "\n" );
document.write( "* If E is the midpoint of DF, then EF = DE\r<BR>\n" );
document.write( "\n" );
document.write( "* **Therefore, EF = 12**\r<BR>\n" );
document.write( "\n" );
document.write( "**Summary:**\r<BR>\n" );
document.write( "\n" );
document.write( "* x = 2<BR>\n" );
document.write( "* DE = 12<BR>\n" );
document.write( "* EF = 12 \r<BR>\n" );
document.write( "\n" );
document.write( "Let me know if you have any other questions or problems to solve! <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );