To determine the undefined value for the equation \( 14 = \frac{7x}{9 + 4x} \), we need to find values of \( x \) that would make the denominator equal to zero, as division by zero is undefined.
The denominator is \( 9 + 4x \). Setting it equal to zero:
\[ 9 + 4x = 0 \]
Solving for \( x \):
\[ 4x = -9 \ x = -\frac{9}{4} \]
Thus, the undefined value occurs when \( x = -\frac{9}{4} \).
Since the options provided do not directly mention \( x = -\frac{9}{4} \), we can evaluate the options given:
- x ≠ 0 - This is incorrect, as \( x = 0 \) does not make the denominator zero.
- x ≠ 94 - This is irrelevant to the problem; \( x = 94 \) does not affect the denominator.
- x ≠ −49 - Also incorrect; \( x = -49 \) does not make the denominator zero.
- x ≠ −94 - Again, this does not affect the denominator.
None of the given choices specify the correct value, which should be \( x \neq -\frac{9}{4} \).
Thus, none of the responses are correct based on the equation provided.