To solve the equation \( 4x - 4 = -24 \), follow these steps:
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Add 4 to both sides of the equation:
\[ 4x - 4 + 4 = -24 + 4 \]
This simplifies to:
\[ 4x = -20 \]
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Now, divide both sides by 4:
\[ \frac{4x}{4} = \frac{-20}{4} \]
This simplifies to:
\[ x = -5 \]
Thus, the solution is:
\[ \boxed{-5} \]