Possible Side Length of Triangle

A triangle has sides of length 7, 24, and x. What is the range of possible values for x?

Recall the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, you need to evaluate the inequalities involving the sides 7 and 24, and x.

Using the triangle inequality, we can establish the following inequalities:

1. $7 + 24 > x$

2. $7 + x > 24$

3. $24 + x > 7$

Use these inequalities to determine the valid range for x.