To solve the equation \( \frac{15}{3x} - 9 - 4 = 12 \), we will first simplify and rearrange the equation.
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Combine terms on the left side:
\[ \frac{15}{3x} - 13 = 12 \]
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Add 13 to both sides:
\[ \frac{15}{3x} = 12 + 13 \]
\[ \frac{15}{3x} = 25 \]
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Multiply both sides of the equation by \( 3x \):
\[ 15 = 25 \cdot 3x \]
\[ 15 = 75x \]
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Divide both sides by 75:
\[ x = \frac{15}{75} \]
\[ x = \frac{1}{5} \]
Now, we need to consider the condition \( x \neq \ldots \).
Since \( 3x \) cannot be zero (as it would make the denominator zero in the original equation), we find:
\[ 3x \neq 0 \implies x \neq 0 \]
Thus, the value that completes the set of equations is:
\[ x \neq 0 \]
In conclusion, the complete statement is:
The value that completes the set of equations is \( x \neq 0 \).