To determine the undefined value for the equation \( 14 = \frac{7x}{9} + 4x \), we first need to solve the equation for \( x \).
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Start with the given equation: \[ 14 = \frac{7x}{9} + 4x \]
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To combine the terms on the right side, we can rewrite \( 4x \) with a common denominator: \[ 4x = \frac{36x}{9} \] Therefore, the equation becomes: \[ 14 = \frac{7x + 36x}{9} \] or \[ 14 = \frac{43x}{9} \]
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Next, we can multiply both sides of the equation by 9 to eliminate the fraction: \[ 14 \cdot 9 = 43x \] Simplifying that gives: \[ 126 = 43x \]
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Now solve for \( x \): \[ x = \frac{126}{43} \]
This indicates that \( x \) can take a specific value, which is \( \frac{126}{43} \). As there is no restriction or undefined point in this calculation, we examine whether we have any restrictions when setting the original equation.
The given equation has no division by zero or any other operations that would lead to an undefined value provided that \( x \) is a real number. Therefore, we check the answer choices:
- A) \( x \neq \frac{9}{4} \)
- B) \( x \neq -\frac{9}{4} \)
- C) \( x \neq 0 \)
- D) \( x \neq -\frac{4}{9} \)
Since none of these values make the equation undefined, the choices provided may not fit directly.
However, since we solved for \( x \) and obtained \( \frac{126}{43} \), this implies that there are specific values of \( x \) that the equation does not take based on integer simplifications. Since they are not relevant to \( x \) or whether it's defined, the nature of the original problem appears irrelevant to the set defined in the responses.
The fact that there's no criterion for undefined values here means none of the responses are correct for the original equation.