document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016849>Question 1016849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 17 inches and a second side that is 1 inch less than twice the third side, what are the possible lengths for the second and third sides?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633226 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=633226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B1%5D+=+17 ALIGN=MIDDLE  ALT=\"s%5B1%5D+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B2%5D+=+2s%5B3%5D-1 ALIGN=MIDDLE  ALT=\"s%5B2%5D+=+2s%5B3%5D-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Case 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B1%5D+%2B+s%5B2%5D+%3E+s%5B3%5D ALIGN=MIDDLE  ALT=\"s%5B1%5D+%2B+s%5B2%5D+%3E+s%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't give any insight, since it reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B3%5D+%3E+-16 ALIGN=MIDDLE  ALT=\"s%5B3%5D+%3E+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is always true.\r<BR>\n" );
document.write( "\n" );
document.write( "Case 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B1%5D+%2B+s%5B3%5D+%3E+s%5B2%5D ALIGN=MIDDLE  ALT=\"s%5B1%5D+%2B+s%5B3%5D+%3E+s%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > will lead, upon the proper substitution, to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17+%2B+s%5B3%5D+%3E+2s%5B3%5D-1 ALIGN=MIDDLE  ALT=\"17+%2B+s%5B3%5D+%3E+2s%5B3%5D-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%3E+s%5B3%5D ALIGN=MIDDLE  ALT=\"18+%3E+s%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Case 3:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B3%5D+%2B+s%5B2%5D+%3E+s%5B1%5D ALIGN=MIDDLE  ALT=\"s%5B3%5D+%2B+s%5B2%5D+%3E+s%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%5B3%5D-1%2Bs%5B3%5D+%3E17 ALIGN=MIDDLE  ALT=\"2s%5B3%5D-1%2Bs%5B3%5D+%3E17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%5B3%5D+%3E+18 ALIGN=MIDDLE  ALT=\"3s%5B3%5D+%3E+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B3%5D+%3E+6 ALIGN=MIDDLE  ALT=\"s%5B3%5D+%3E+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%3E+s%5B3%5D+%3E+6 ALIGN=MIDDLE  ALT=\"18+%3E+s%5B3%5D+%3E+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B3%5D+=+%28s%5B2%5D%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"s%5B3%5D+=+%28s%5B2%5D%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and so substitution into the last inequality and simplifying yields\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+%3E+s%5B2%5D+%3E+11 ALIGN=MIDDLE  ALT=\"35+%3E+s%5B2%5D+%3E+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );