To solve the equation \( 4x - 9 = -49 \), follow these steps:
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Add 9 to both sides of the equation:
\[ 4x - 9 + 9 = -49 + 9 \]
This simplifies to:
\[ 4x = -40 \]
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Next, divide both sides by 4 to isolate \( x \):
\[ x = \frac{-40}{4} \]
This simplifies to:
\[ x = -10 \]
Thus, the solution is \( \boxed{-10} \).