To solve the equation
\[ \frac{12 - x}{9} = 11, \]
follow these steps:
- Start by eliminating the fraction by multiplying both sides by 9:
\[ 12 - x = 11 \cdot 9. \]
- Calculate \(11 \cdot 9\):
\[ 11 \cdot 9 = 99, \]
so the equation simplifies to:
\[ 12 - x = 99. \]
- Next, isolate \(x\) by subtracting 12 from both sides:
\[ -x = 99 - 12, \]
which simplifies to:
\[ -x = 87. \]
- Multiply both sides by -1 to solve for \(x\):
\[ x = -87. \]
Therefore, the solution is
\[ \boxed{-87}. \]