SOLUTION: Two sides of a triangle have lengths 6 and 8. What lengths are possible for the third side? Explain.

If two sides of a triangle have lengths a and b, then the
length, c, of the third side must be between |a-b| and a+b,
exclusive of each.  That is 

       |a-b| < c < a+b 

Therefore,

If two sides of a triangle have lengths 6 and 8, then the
length, c, of the third side must be between |6-8| and 6+8,
exclusive of each.  That is 

       |6-8| < c < 6+8

        |-2| < c < 14
  
           2 < c < 14

So the third side must be longer than 2 yet shorter than 14.

Edwin