To find the undefined value for the equation \( 14 = 7 \times 9 + 4x \), we first solve for \( x \).
- Calculate \( 7 \times 9 \): \[ 7 \times 9 = 63 \]
- Substitute into the equation: \[ 14 = 63 + 4x \]
- Rearranging the equation to isolate \( 4x \): \[ 4x = 14 - 63 \] \[ 4x = -49 \]
- Now, solving for \( x \): \[ x = \frac{-49}{4} \]
Thus, the equation does not become undefined for any specific value of \( x \) in the context of a simple linear equation, as \( x \) can take on any value except where the context specifies.
From the provided multiple choice answers, we look for the one that implies a restriction or leads to a contradiction:
The answer choices include:
- \( x \neq 94 \)
- \( x \neq \frac{9}{4} \)
- \( x \neq -\frac{9}{4} \)
- \( x \neq -49 \)
- \( x \neq 0 \)
Since our solution is \( x = -\frac{49}{4} \), there are no conflicting values provided that would make the equation undefined.
However, if we were to consider an interpretation of "undefined" in the form of an irrelevant distraction, the closest is that if any value could trigger an undefined behavior it might lead someone to think about potential division by zero situations or singularities, yet in the context here, this does appear to be resolved straightforwardly.
Since the original equation involves multiplying and the addition or subtraction of constants rather than division, every value of \( x \) remains valid except in scenarios that would create inconsistencies under further context (which aren't defined here).
Thus, the undefined responses do not seem to make sense relative to what we have. Therefore, there is no explicit undefined response here according to the presented options—none must apply based on the equation unless additional context discusses specific scenarios, which we do not explicitly have.
In pure algebraic terms, we'd conclude that none of those choices are valid restrictions based on the established mathematics.