document.write( "Question 704405: given the three side lengths of triangle ABC which are 13-x, 6+x, and 15 what are all the possible vaules of X? \n" ); document.write( "
Algebra.Com's Answer #434071 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If the three sides of a triangle are a,b, and c, then\r\n" );
document.write( "the triangular inequality states:\r\n" );
document.write( "\r\n" );
document.write( "a + b > c\r\n" );
document.write( "a + c > b\r\n" );
document.write( "b + c > a\r\n" );
document.write( "\r\n" );
document.write( "Here we have\r\n" );
document.write( "\r\n" );
document.write( "Side a = 13-x, \r\n" );
document.write( "Side b = 6+x,\r\n" );
document.write( "Side c = 15\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The sum of each pair of sides is greater than the third side, so there\r\n" );
document.write( "are three possibilities\r\n" );
document.write( "\r\n" );
document.write( "a + b > c\r\n" );
document.write( "\r\n" );
document.write( "(13-x)+(6+x) > 15\r\n" );
document.write( "13-x+6+x > 15\r\n" );
document.write( "19 > 15\r\n" );
document.write( "\r\n" );
document.write( "That would be true regardless of what x is, so any\r\n" );
document.write( "restrictions on x will comes from the other two\r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "a + c > b\r\n" );
document.write( "\r\n" );
document.write( "(13-x)+15 > 6+x\r\n" );
document.write( "13-x+15 > 6+x\r\n" );
document.write( "28-x > 6+x\r\n" );
document.write( "-2x > -22\r\n" );
document.write( "x < 11    (the inequality reverses when dividing by a negative)\r\n" );
document.write( "\r\n" );
document.write( "So that's one restriction on x  \r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "b + c > a\r\n" );
document.write( "\r\n" );
document.write( "(6+x)+15 > 13-x\r\n" );
document.write( "6+x+15 > 13-x\r\n" );
document.write( "21+x > 13-x\r\n" );
document.write( "2x > -8\r\n" );
document.write( "x > -4\r\n" );
document.write( "\r\n" );
document.write( "That's another restriction on x\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Put those restrictions toget0her\r\n" );
document.write( "\r\n" );
document.write( "x < 11 and x > -4\r\n" );
document.write( "\r\n" );
document.write( "Turn x > -4 around as -4 < x since it is equivalent\r\n" );
document.write( "and we can then write that as a continued inequality\r\n" );
document.write( "with x in the middle:\r\n" );
document.write( "\r\n" );
document.write( "-4 < x < 11\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );