document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119574>Question 1119574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These conditions were given:\r<BR>\n" );
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document.write( "AC + BC > AB 1st Triangle Inequality condition <BR>\n" );
document.write( "AB + BC > AC 2nd Triangle Inequality condition <BR>\n" );
document.write( "AB + AC > BC 3rd Triangle Inequality condition <BR>\n" );
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document.write( "Activity: The sum of the lengths of any two sides of a triangle is greater<BR>\n" );
document.write( "than the length of the third side. What can you conclude about AC in<BR>\n" );
document.write( "&#8710;ABC? (Hint: Use the above example as a guideline.) \r<BR>\n" );
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document.write( "1. AB = 6; BC + 2AC = 18 (5 pts) \r<BR>\n" );
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document.write( "  BC + 2AC = 18 > 6  (I know it seems very wrong but I couldn't understand it)  <BR>\n" );
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document.write( "2. BC = 7;  AC = 2 + AB (5 pts) \r<BR>\n" );
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document.write( "  2 + AB > 7 <BR>\n" );
document.write( "  <BR>\n" );
document.write( "3. AB + AC = 5; AC + BC = 4 (5 pts) \r<BR>\n" );
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document.write( "  AB + AC = 5 > AB + BC = 4<BR>\n" );
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document.write( "4. BC + AC = 22; AB + BC = 12 (5 pts)\r<BR>\n" );
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document.write( "  BC + AC = 22 > AB + BC =12\r<BR>\n" );
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document.write( "Please show your work so I can understand it better, thank you. \r<BR>\n" );
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document.write( "Did I write my inequalities correctly?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735489 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">I will only do the first one.\r\n" );
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document.write( "These conditions were given:\r<BR>\n" );
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document.write( "AC + BC > AB 1st Triangle Inequality condition <BR>\n" );
document.write( "AB + BC > AC 2nd Triangle Inequality condition <BR>\n" );
document.write( "AB + AC > BC 3rd Triangle Inequality condition <BR>\n" );
document.write( " <BR>\n" );
document.write( "Activity: The sum of the lengths of any two sides of a triangle is greater<BR>\n" );
document.write( "than the length of the third side. What can you conclude about AC in<BR>\n" );
document.write( "&#8710;ABC? (Hint: Use the above example as a guideline.) \r<BR>\n" );
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document.write( "1. AB = 6; BC + 2AC = 18 (5 pts) <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "BC + 2AC = 18\r\n" );
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document.write( "Solve for BC\r\n" );
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document.write( "BC = 18 - 2AC\r\n" );
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document.write( "Substitute AB = 6 and BC = 18 - 2AC in:\r\n" );
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document.write( "AC + BC > AB 1st Triangle Inequality condition\r\n" );
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document.write( "AC + (18 - 2AC) > 6\r\n" );
document.write( "  AC + 18 - 2AC > 6\r\n" );
document.write( "       -AC + 18 > 6\r\n" );
document.write( "            -AC > -12\r\n" );
document.write( "             AC < 12\r\n" );
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document.write( "Next, substitute AB = 6 and BC = 18 - 2AC in\r\n" );
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document.write( "AB + BC > AC 2nd Triangle Inequality condition\r\n" );
document.write( "6 + (18 - 2AC) > AC\r\n" );
document.write( "  6 + 18 - 2AC > AC\r\n" );
document.write( "      24 - 2AC > AC\r\n" );
document.write( "            24 > 3AC\r\n" );
document.write( "             8 > AC\r\n" );
document.write( "            AC < 8\r\n" );
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document.write( "Finally, substitute AB = 6 and BC = 18 - 2AC in\r\n" );
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document.write( "AB + AC > BC 3rd Triangle Inequality condition \r\n" );
document.write( " 6 + AC > 18 - 2AC\r\n" );
document.write( "    -12 > -3AC\r\n" );
document.write( "      4 < AC\r\n" );
document.write( "     AC > 4\r\n" );
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document.write( "So putting all three results together\r\n" );
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document.write( "AC < 12, AC < 8, and AC > 4\r\n" );
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document.write( "Since AC is less than 8, it's automatically less than 12,\r\n" );
document.write( "so we can dispense with AC < 12.  So we have:\r\n" );
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document.write( "AC < 8 and AC > 4  which can be combined and written as\r\n" );
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document.write( "    4 < AC < 8    [that is, AC is between 4 and 8]\r\n" );
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document.write( "--------------\r\n" );
document.write( "Do the others the same way.  \r\n" );
document.write( "1.  Solve the given equation for the side other than AC.  \r\n" );
document.write( "2.  Substitute in each of the Triangle Inequality conditions.\r\n" );
document.write( "3.  Solve for AC in each.\r\n" );
document.write( "4.  Consider the three inequalities together. \r\n" );
document.write( "5.  Give the inequality interval for AC.\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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