To solve for \( x \) in the rectangle BCDA with points E, B, and C, where \( BE = 2x + 9 \) and \( EC = 12x - 11 \), we need to notice that \( BE + EC \) must equal the total length of the side \( BC \).
Since BC is a side of the rectangle and consists of BE and EC, we can set up the equation as follows:
\[ BE + EC = BC \]
Assuming BC is the full length from B to C, we can express:
\[ 2x + 9 + 12x - 11 = BC \]
Combine like terms:
\[ (2x + 12x) + (9 - 11) = BC \] \[ 14x - 2 = BC \]
Since BC is the length from B to C, we may need the specific length of BC to proceed further. However, if we assume that the length doesn’t need to be provided and we can equate the two expressions, we can establish an equation where the total lengths are equal.
If \( BE + EC \) is all of BC, we can find \( x \):
Setting \( BE + EC = 0 \) or any other assumption if lengths are known would yield:
Equate:
\[ 2x + 9 = 12x - 11 \]
Solving for \( x \):
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Rearrange the equation to isolate \( x \): \[ 9 + 11 = 12x - 2x \] \[ 20 = 10x \]
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Divide by 10: \[ x = 2 \]
The value of \( x \) is \( \boxed{2} \).
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