To solve for \( x \) in the rectangle \( BCDA \) where \( BE = 2x + 9 \) and \( EC = 12x - 11 \), we can use the fact that \( BE + EC = BC \).
Since \( E \) is a point on line segment \( BC \), we can set up the equation:
\[ BE + EC = BC. \]
Assuming \( BC \) has the same length regardless of the values of \( x \) in the expressions for \( BE \) and \( EC \), we set \( BE \) equal to \( EC \):
\[ 2x + 9 = 12x - 11. \]
Now, we can solve for \( x \):
- Rearrange the equation to isolate \( x \):
\[ 9 + 11 = 12x - 2x, \]
\[ 20 = 10x. \]
- Divide both sides by 10:
\[ x = 2. \]
Thus, the value of \( x \) is \( \boxed{2} \).