To solve the equation \( 4x - 3 = 3x - 9 \), follow these steps:
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Subtract \( 3x \) from both sides: \[ 4x - 3x - 3 = -9 \] This simplifies to: \[ x - 3 = -9 \]
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Next, add \( 3 \) to both sides: \[ x - 3 + 3 = -9 + 3 \] This simplifies to: \[ x = -6 \]
Thus, the solution is: \[ \boxed{-6} \]