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To find the undefined value for the equation
\[
22 = 4 + \frac{5x}{9x - 6},
\]
we need to determine when the fraction \(\frac{5x}{9x - 6}\) is undefined. A fraction is undefined when its denominator is equal to zero. Thus, we set the denominator equal to zero and solve for \(x\):
\[
9x - 6 = 0.
\]
Adding 6 to both sides gives:
\[
9x = 6.
\]
Now, dividing both sides by 9:
\[
x = \frac{6}{9} = \frac{2}{3}.
\]
So, the undefined value for \(x\) is
\[
\frac{2}{3}.
\]
Thus, the answer is:
\[
\frac{2}{3}.
\]