To solve for \( x \) in the equation
\[ -6.29(x + 7.85) = -19.499, \]
first, divide both sides by \(-6.29\):
\[ x + 7.85 = \frac{-19.499}{-6.29}. \]
Calculating the right side:
\[ \frac{-19.499}{-6.29} \approx 3.098. \]
Now we have:
\[ x + 7.85 \approx 3.098. \]
Next, subtract \( 7.85 \) from both sides:
\[ x \approx 3.098 - 7.85, \] \[ x \approx -4.752. \]
Thus, the solution for \( x \) is approximately
\[ \boxed{-4.752}. \]