To identify the undefined value for the equation \( 14 = 7 \times 9 + 4x \), we first need to manipulate the equation to isolate \( x \).
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Start with the equation:
\[ 14 = 7 \times 9 + 4x \]
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Calculate \( 7 \times 9 \):
\[ 7 \times 9 = 63 \]
So the equation becomes:
\[ 14 = 63 + 4x \]
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Subtract 63 from both sides:
\[ 14 - 63 = 4x \]
Which simplifies to:
\[ -49 = 4x \]
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Now, divide both sides by 4 to solve for \( x \):
\[ x = \frac{-49}{4} \]
The only value that would cause the equation to be undefined for \( x \) would come from the term where \( x \) is in the denominator. However, because there is no denominator present in the equation we are solving, the expression is defined for all values of \( x \).
Given the options in your question, none of them actually represent a scenario of undefined values in the context of the equation provided.
However, purely from the context based on standard options, typically when solving for \( x \), the undefined might refer to can sometimes originate from divisions by zero, but that does not apply here. Still, the calculated result \( x = \frac{-49}{4} \) does not define any restriction.
So, if we take it as "what value should \( x \) not equal to prevent issues in similar expressions when x is in a denominator," we could argue for that scenario, otherwise x can take values freely in this situation without causing undefined behavior.
Conclusion: Among the options, if you are looking for a numerical response that illustrates how \( x \) could potentially be undefined based on contextual meaning, an argument could be made against responses equating it to certain rational values but none accurately represent the undefined parameter related to dynamics of division. Thus providing an overall observation, you're prompted to investigate further vocalizing and reformulating rational discourse for conceptual clarity over undefined circumstances usually attached to algebraic expressions.