To solve the equation \( \frac{15}{3x} - 9 - 4 = 12 \), we can first simplify it step-by-step.
-
Combine like terms on the left side: \[ \frac{15}{3x} - 13 = 12 \]
-
Add 13 to both sides: \[ \frac{15}{3x} = 12 + 13 \] \[ \frac{15}{3x} = 25 \]
-
Now, we can cross-multiply: \[ 15 = 25 \cdot 3x \] \[ 15 = 75x \]
-
Divide both sides by 75: \[ x = \frac{15}{75} \] \[ x = \frac{1}{5} \]
Now, the problem states \( x \neq \) ___, which means we must also consider any values that would make the original expression undefined.
The term \( \frac{15}{3x} \) is undefined when \( 3x = 0 \), which gives \( x = 0 \). Therefore, while we found that \( x = \frac{1}{5} \) makes the equation true, we also identify \( x \) cannot be 0 to prevent division by zero.
Thus, the value that completes the set of equations is \( x \neq 0 \).
Final answer: \[ x \neq 0 \]