Answer: 9
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Step-by-step explanation:
The segment (4x-9) units long is the midsegment of the triangle. This is because each endpoint is a midpoint of the slanted sides.
One property of midsegments is that it is half as long as the side parallel to it.
The (4x-9) side is half as long compared to the 6x side.
Rephrased another way: The 6x is twice as long compared to (4x-9)
We'll use this to set up the equation to solve for x.
6x = 2*(4x-9)
6x = 8x-18
6x-8x = -18
-2x = -18
x = -18/(-2)
x = 9 is the final answer