Triangle Inequality and Valid Values of x

In triangle ABC, the lengths of sides AB, AC, and BC are represented by 5x, 2x + 3, and 3x - 1 respectively.

Determine the value of x such that triangle ABC adheres to the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

List the valid values of x that satisfy these conditions and determine:

Quantity A: The number of valid values of x.

Quantity B: 2.