Answer:
x = 7
Step-by-step explanation:
See the attached figure.
As shown: A C D F is a trapezoid and BE is a mid-segment.
The mid-segment of the trapezoid is the average of its bases.
BE = 0.5 ( A F + C D)
Given: CD = 18 , BE = 2x + 10 and A F = 6x - 12
So,
2x + 10 = 0.5 ( 18 + 6x - 12)
Solve for x
2x + 10 = 0.5 (6 + 6x)
2x + 10 = 3 + 3x
10 - 3 = 3x - 2x
∴ x = 7
So, the value of x is 7
