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To solve the equation \( 153x - 9 - 4 = 12 \), we first simplify it.
Combine the constants on the left side:
\[
153x - 13 = 12
\]
Next, we add 13 to both sides of the equation:
\[
153x = 12 + 13
\]
\[
153x = 25
\]
Now, we divide both sides by 153:
\[
x = \frac{25}{153}
\]
The question asks for the value that completes the set of equations in the form \( x \neq \_\_\_\_ \).
Since no values were excluded in the given equation, we simply note that \( x \) cannot take any other form. Hence, the value that completes the set of equations is:
\[
x \neq \frac{25}{153}
\]
So, the answer is \( x \neq \frac{25}{153} \).