To find the undefined value in the equation \( 14 = \frac{7x}{9} + 4x \), we first need to solve for \( x \).
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Rewrite the equation by finding a common denominator for the terms on the right side:
\[ 14 = \frac{7x}{9} + \frac{36x}{9} \]
This simplifies to:
\[ 14 = \frac{7x + 36x}{9} \] \[ 14 = \frac{43x}{9} \]
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Multiply both sides by 9 to eliminate the fraction:
\[ 9 \cdot 14 = 43x \] \[ 126 = 43x \]
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Now, divide both sides by 43 to solve for \( x \):
\[ x = \frac{126}{43} \]
Now, let's analyze the equation to check for any undefined values. The only potential undefined values in terms of rational expressions typically arise from division by zero.
In our original equation, there is no division by a variable term, so the solutions will always yield a definite value of \( x \).
Therefore, there are no undefined values arising from this specific equation.
None of the choices \( x \neq 0 \), \( x \neq \frac{9}{4} \), \( x \neq -\frac{4}{9} \), or \( x \neq -\frac{9}{4} \) are relevant to this context.
So, the answer is that there is no undefined value for this equation, meaning none of the provided options are correct in this case based on the equation without deriving an undefined scenario.
If this was a multiple choice question expecting to find possible exclusions, you may consider those values irrelevant as no \( x \) leads to undefined behavior in the equation provided.