Geometry

Question Analysis：
This question involves applying the midsegment theorem of a trapezoid using algebra.
The main focus is on setting up and solving an equation based on the average of the two bases.

Key Concept Explanation：
In a trapezoid, the midsegment (or median) is a segment connecting the midpoints of the non-parallel sides.
The length of the midsegment is the average of the lengths of the two bases

Step-by-Step Solution：
Apply the midsegment formula:
9x − 2 = [(4x + 8) + (6x + 12)]/2
9x − 2 = (10x + 20)/2 = 5x + 10
9x − 2 = 5x + 10 ⇒ 4x = 12 ⇒ x = 3

Common Mistakes：
Confusing the midsegment with a side length, not applying the average formula.
Incorrectly combining like terms when simplifying expressions.
Assuming midsegment formula uses subtraction instead of addition.