To solve the equation \(-6.29(x + 7.85) = -19.499\), we'll start by simplifying and isolating \(x\).
- Distribute \(-6.29\) on the left side:
\[ -6.29x - 6.29 \cdot 7.85 = -19.499 \]
Calculating \(-6.29 \cdot 7.85\):
\[ -6.29 \cdot 7.85 \approx -49.2905 \]
So the equation becomes:
\[ -6.29x - 49.2905 = -19.499 \]
- Add \(49.2905\) to both sides to isolate the term with \(x\):
\[ -6.29x = -19.499 + 49.2905 \]
Calculating the right side:
\[ -19.499 + 49.2905 \approx 29.7915 \]
Now we have:
\[ -6.29x = 29.7915 \]
- Next, divide both sides by \(-6.29\):
\[ x = \frac{29.7915}{-6.29} \]
Calculating this gives:
\[ x \approx -4.74 \]
Thus, the solution for \(x\) is:
\[ \boxed{-4.74} \]