Geometry

Question Analysis:
This question tests knowledge of parallelogram conditions.
The main focus is recognizing that a single pair of parallel and equal-length sides confirms a parallelogram.

Key Concept Explanation:
A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and equal in length.
Here, sides PQ and SR are already parallel, so we must find the value of x that makes them equal in length.

Step-by-Step Solution:
Set the expressions for the opposite sides equal: 3x + 1 = 5x - 7
Subtract 3x from both sides: 1 = 2x - 7
Add 7 to both sides: 8 = 2x
Divide both sides by 2: x = 4

Com...