document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917636>Question 917636</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 18 inches and a second side that is 3 inches 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 #556758 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=556758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Description of the sides of your triangle:<BR>\n" );
document.write( "18; and -3+2x; and x.\r<BR>\n" );
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document.write( "According to the THEOREM you quoted, picking any two sides should conform to the theorem as stated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3%2Bx%3E18 ALIGN=MIDDLE  ALT=\"2x-3%2Bx%3E18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, picking the side #2 and side #3 to compare to side #1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-3%3E18 ALIGN=MIDDLE  ALT=\"3x-3%3E18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%3E21 ALIGN=MIDDLE  ALT=\"3x%3E21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E7 ALIGN=MIDDLE  ALT=\"x%3E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E7%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you also need to examine comparing sum of sides 1 and 3 with length of side 2, using the triangle inequality theorem.  THEN take the values for x which satisfy BOTH inequalities.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Bx%3E2x-3 ALIGN=MIDDLE  ALT=\"18%2Bx%3E2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2B3%3Ex ALIGN=MIDDLE  ALT=\"18%2B3%3Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%3Ex ALIGN=MIDDLE  ALT=\"21%3Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Do one more just to be certain.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2B2x-3%3Ex ALIGN=MIDDLE  ALT=\"18%2B2x-3%3Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Bx-3%3E0 ALIGN=MIDDLE  ALT=\"18%2Bx-3%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E-15 ALIGN=MIDDLE  ALT=\"x%3E-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is not very meaningful.\r<BR>\n" );
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document.write( "The <b>intersection</b> of all three solutions is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E21%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Side number 2 would be 2x-3 for x>21,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A21-3 ALIGN=MIDDLE  ALT=\"2%2A21-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is 39 at its limit. </SPAN>\n" );
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