Since EF is the median of trapezoid ABCD, it is also equal to the average of the lengths of the bases AB and DC.
That is, EF = (AB + DC) / 2
Substituting the given values, we get:
2x + 2 = (5x - 9 + x + 3) / 2
Multiplying both sides by 2 to eliminate the fraction, we get:
4x + 4 = 6x - 6
Subtracting 4x from both sides, we get:
4 = 2x - 6
Adding 6 to both sides, we get:
10 = 2x
Dividing both sides by 2, we get:
x = 5
Therefore, the value of x is 5.