document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944040>Question 944040</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangles: The sum of the lengths of any two sides of a triangle must be greater than the third side. A triangle has sides as follows: the first side is 18 mm and the second side is 3 mm more than twice the third side. What are the possible lengths of the second and third sides? [hint: You will need to solve two inequalities.]\r<BR>\n" );
document.write( "\n" );
document.write( "I figured out what the second and third sides have to be more than 13 mm and 5 mm, respectively. (I did this by setting the inequality to x + 2x + 3 > 18) I got the answer half correct; but I do not understand how to get the value the second and third sides have to be less than. Please help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575602 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=575602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> UNDERSTANDING the triangle inequality theorem is necessary.  Use it to formulate the inequalities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the \"third\" side length be x.<BR>\n" );
document.write( "The first two lengths of the triangle sides are 18 and 3+2x.  Those are directly from the description.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, form the inequality statements using the theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2818%2B2x%2B3%3Ex%2C18%2Bx%3E2x%2B3%2C2x%2B3%2Bx%3E18%29 ALIGN=MIDDLE  ALT=\"system%2818%2B2x%2B3%3Ex%2C18%2Bx%3E2x%2B3%2C2x%2B3%2Bx%3E18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify the system:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2821%3E-x%2C15%3Ex%2C3x%3E15%29 ALIGN=MIDDLE  ALT=\"system%2821%3E-x%2C15%3Ex%2C3x%3E15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first simplified inequality does not help any.<BR>\n" );
document.write( "The next two are these:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%3C15%2Cx%3E5%29 ALIGN=MIDDLE  ALT=\"system%28x%3C15%2Cx%3E5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, when simplified.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solution in more condensed form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%285%3Cx%3C15%29 ALIGN=MIDDLE  ALT=\"highlight%285%3Cx%3C15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the third side. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );