To find the undefined value for the equation \( 14 = 7x + 4x \), it's important to first simplify and solve the equation.
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Combine like terms: \[ 14 = (7x + 4x) \Rightarrow 14 = 11x \]
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Solve for \( x \): \[ x = \frac{14}{11} \]
Since the equation is simplified and solved directly, there are no values of \( x \) that cause any denominator to be zero or an operation to be undefined. Therefore, the equation is defined for all values of \( x \).
However, if the question is looking for a form of expression that represents restrictions typically found in rational equations (where there could be division by zero), it's possible we might have missed something.
Based on the provided potential responses:
- \( x \neq \frac{-9}{4} \)
- \( x \neq \frac{-4}{9} \)
- \( x \neq \frac{9}{4} \)
- \( x \neq 0 \)
None of these options correspond to the solution derived from the equation \( x = \frac{14}{11} \).
If we are strictly looking for undefined or excluded values in a rational expression scenario, we'd evaluate only if \( x \) can yield a denominator of zero, but here it appears there was no such scenario provided.
In this case, the response is aimed at values that the problem specifies and since there's no fraction or zero Division arising from \( 11x \), no clear solution is found that matches the criteria stated in the options.
Therefore, technically speaking based on the derived solution and provided choices, the answer that is closest to acknowledging any restrictions in mathematical terms is likely to be:
- \( x \neq 0 \).
This is observed often in various equation claims or restrictions but doesn’t arise from the workings of \( 14=11x \) materially.