Let's solve the equation step by step:
The equation given is:
\[ \frac{15}{3x} - 9 - 4 = 12 \]
First, let’s simplify the left side:
\[ \frac{15}{3x} - 13 = 12 \]
Next, add 13 to both sides:
\[ \frac{15}{3x} = 12 + 13 \] \[ \frac{15}{3x} = 25 \]
To eliminate the fraction, multiply both sides by \(3x\):
\[ 15 = 25 \cdot 3x \]
Now, simplify the right-hand side:
\[ 15 = 75x \]
Next, we solve for \(x\) by dividing both sides by 75:
\[ x = \frac{15}{75} \]
Simplifying the fraction gives:
\[ x = \frac{1}{5} \]
Finally, we note any restrictions. Since \(x\) is in the denominator (\(3x\)), we must ensure \(3x \neq 0\), so \(x\) must not be 0.
Thus, the value that completes the set of equations is:
\[ x = \frac{1}{5} \text{ and } x \neq 0 \]
The final answer is:
\(\frac{1}{5}\)
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