To find the undefined value for the equation \( 14 = \frac{7x}{9 + 4x} \), we need to determine when the denominator of the right-hand side becomes zero, because division by zero is undefined.
The denominator is given by:
\[ 9 + 4x \]
Setting the denominator equal to zero gives:
\[ 9 + 4x = 0 \]
Now, we'll solve for \( x \):
\[ 4x = -9 \] \[ x = -\frac{9}{4} \]
Thus, the undefined value for this equation occurs when \( x = -\frac{9}{4} \). At this value, the expression on the right-hand side becomes undefined.