To solve the equation \( 4x - 3 = 3x - 9 \):
- First, isolate \( x \) by subtracting \( 3x \) from both sides:
\[ 4x - 3x - 3 = -9 \]
This simplifies to:
\[ x - 3 = -9 \]
- Next, add 3 to both sides to solve for \( x \):
\[ x = -9 + 3 \] \[ x = -6 \]
The solution is:
\[ \boxed{-6} \]
So the answer is \( x = -6 \) (or "x equals negative 6").