document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71920>Question 71920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is how to solve: <BR>\n" );
document.write( "2x+1<3x<12\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51438 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x+1<3x<12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Split this into two problems.  The first problem is <BR>\n" );
document.write( ".<BR>\n" );
document.write( "2x + 1 < 3x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 2x from both sides and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "+1 < x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This tells you that x must be greater than +1.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's work the second problem.  It is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3x < 12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Dividing both sides by +3 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x < +4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So on one hand, x must be greater than +1, but on the other hand x must be less than +4.<BR>\n" );
document.write( "We can write this as:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "+1 < x < +4<BR>\n" );
document.write( ".<BR>\n" );
document.write( "As a check you can select some values of x between +1 and +4 and plug them in to the original<BR>\n" );
document.write( "problem.  For example, let's try x = +2. Using this value, the original problem becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2x + 1 < 3x < 12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2(+2) + 1 < 3(+2) < 12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "4 + 1 < 6 < 12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5 < 6 < 12<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That works ... so x = +2 works as a check.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you understand how to work the problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );