document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168553>Question 168553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> absolute value  [2x+1]less than or equal to 11  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124229 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=124229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic formula for solving an inequality is:<BR>\n" );
document.write( "if |x| = d, then x = d, and x = -d<BR>\n" );
document.write( "if |x| < d, then x < d, and x > -d<BR>\n" );
document.write( "if |x| > d, then x > d, and x < -d<BR>\n" );
document.write( "likewise,<BR>\n" );
document.write( "if |x| <= d, then x <= d, and x >= -d<BR>\n" );
document.write( "if |x| >= d, then x >= d, and x >= -d<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if |2x+1| <= 11, then<BR>\n" );
document.write( "2x + 1 <= 11, and 2x + 1 >= -11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "working with 2x + 1 <= 11:<BR>\n" );
document.write( "2x + 1 <= 11<BR>\n" );
document.write( "2x <= 10<BR>\n" );
document.write( "x <= 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "working with 2x + 1 >= -11:<BR>\n" );
document.write( "2x + 1 >= -11<BR>\n" );
document.write( "2x >= -12<BR>\n" );
document.write( "x >= -6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is x <= 5 and x >= -6<BR>\n" );
document.write( "this translates to:<BR>\n" );
document.write( "-6 <= x <= 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to test:<BR>\n" );
document.write( "let x = -7<BR>\n" );
document.write( "|2x+1| = |-14+1| = |-13| = 13 NOT <= 11 = ok since -7 is not >= -6 which violates one of the conditions.<BR>\n" );
document.write( "let x = 6<BR>\n" );
document.write( "|2x+1| = |12+1| = |13| = 13 NOT <= 11 = ok since 6 is not <= 5 which violates one of the conditions.<BR>\n" );
document.write( "let x = -6<BR>\n" );
document.write( "|2x+1| = |-12+1| = |-11| = 11 <= 11 = ok since -6 = -6 which is one of the conditions.<BR>\n" );
document.write( "let x = 5<BR>\n" );
document.write( "|2x+1| = |10+1| = |11| = 11 <= 11 = ok since 5 = 5 which is one of the conditions.<BR>\n" );
document.write( "let x = 0<BR>\n" );
document.write( "|2x+1| = |-+1| = |1| = 1 <= 11 = ok since 1 > -6 and < 5 which is one of the conditions.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer proves to be good.<BR>\n" );
document.write( "|2x-1| <= 11 is a true equation when:<BR>\n" );
document.write( "-6 <= x <= 5<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );