To find the values of \( x \) that would make the equation \( 14 = \frac{7x}{9 + 4x} \) undefined, we need to look at the expression \( \frac{7x}{9 + 4x} \).
The expression becomes undefined when the denominator is equal to zero. Thus, we set the denominator equal to zero and solve for \( x \):
\[ 9 + 4x = 0 \] \[ 4x = -9 \] \[ x = -\frac{9}{4} \]
So, the value of \( x \) that makes the equation undefined is:
\[ x \neq -\frac{9}{4} \]
The other options listed (like \( x \neq 0 \) and \( x \neq -\frac{4}{9} \)) are not relevant to the equation being undefined. Therefore, the correct answer is:
x ≠ -9/4 (x does not equal negative 9 over 4).