Inequalities in Triangle Sides

Consider triangle ABC where the lengths of the sides are given as follows:

AB = 7, BC = 24, and AC = x, where x represents an unknown length.

The area of triangle ABC can be calculated using Heron's formula, which states that the area can be found using the semi-perimeter:

$$s = \f\frac{AB + BC + AC}{2} = \f\frac{7 + 24 + x}{2}$$

The area is then determined by:

$$Area = \sqrt{s(s-AB)(s-BC)(s-AC)$$

For triangle ABC to be valid, it must adhere to the triangle inequality theorem. Specifically, the following inequalities must hold:

1. $AB + BC > AC$

2. $AB + AC > BC$

3. $BC + AC > AB$

Using the inequalities above, determine whether the length of side AC ($x$) must be greater than, less than, or equal to a certain quantity derived from the known lengths.