Question 1200101
.
Triangle inequality Theorem, need to make a conclusion about AC

AB + AC = 5;  AC + BC = 4
~~~~~~~~~~~~~~~~~~~~~


<pre>
We are given these two equalities

    AB + AC = 5    (1)

    AC + BC = 4    (2)


Subtract (2) from (1)  (both sides).  The terms "AC" will annihilate, so we will get

    AB - BC = 5 - 4 = 1.    (3)


Due to triangle inequalities,

    | AB - BC | < AC  for any triangle ABC.


So, from (3) we conclude that

    1 < AC,  or  AC > 1.


<U>ANSWER</U>.  From the given equalities, the triangle inequalities imply AC > 1.
</pre>

Solved.