To solve the equation \(4x - 3 = 3x - 9\), we start by isolating the variable \(x\).
First, we can subtract \(3x\) from both sides:
\[ 4x - 3x - 3 = -9 \]
This simplifies to:
\[ x - 3 = -9 \]
Next, we add \(3\) to both sides to isolate \(x\):
\[ x - 3 + 3 = -9 + 3 \]
This simplifies to:
\[ x = -6 \]
Thus, the solution is
\[ \boxed{-6} \]
To verify our solution, we can substitute \(x = -6\) back into the original equation:
\[ 4(-6) - 3 = 3(-6) - 9 \]
Calculating the left side:
\[ 4(-6) - 3 = -24 - 3 = -27 \]
Now, calculating the right side:
\[ 3(-6) - 9 = -18 - 9 = -27 \]
Since both sides are equal, our solution \(x = -6\) is confirmed to be correct:
\[ \boxed{-6} \]
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