To find the value of \(x\) in the equation \(14 = \frac{7x}{9} + 4x\), let's first combine the terms on the right-hand side.
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Rewrite \(4x\) with a common denominator: \[ 4x = \frac{36x}{9} \] (since \(4x\) is the same as \(\frac{4x \cdot 9}{9}\))
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Substitute this back into the equation: \[ 14 = \frac{7x}{9} + \frac{36x}{9} \]
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Combine the fractions: \[ 14 = \frac{7x + 36x}{9} = \frac{43x}{9} \]
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To eliminate the fraction, multiply both sides by 9: \[ 14 \cdot 9 = 43x \] \[ 126 = 43x \]
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Solve for \(x\) by dividing both sides by 43: \[ x = \frac{126}{43} \]
Now, in terms of undefined values, there don't appear to be any restrictions on \(x\) in the context presented. The equation is defined for all real numbers. Therefore, the only undefined context might refer to values that would make division by zero occur, but in this equation, such a situation does not arise.
However, reviewing your responses, it's possible that the question concerns specifically examining if there were any excluded values improperly represented. Still, without additional context or specific exclusions, we can't assign a traditional 'undefined' value based on the operations carried out.
The final answer should indicate that \(x\) is defined through \(x = \frac{126}{43}\), and there are no real exclusions unless specified by a different context.
Given your options, if you have to choose the closest answer based on the case numbers given, you can pick \(x≠0\) since \(x\) must not be zero based on the context of the question being about undefined interaction. However, based on the calculation performed, no specific exclusion directly comes from the operation itself. Always remember, whether checking against multiple-choice responses, reviewing them against calculated properties is essential in answering problems.
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