To solve the equation \( -6.29(x + 7.85) = -19.499 \), follow these steps:
-
Distribute \( -6.29 \) on the left side:
\[ -6.29x - 6.29 \times 7.85 = -19.499 \]
Calculate \( -6.29 \times 7.85 \):
\[ -6.29 \times 7.85 \approx -49.4415 \]
Therefore, the equation becomes:
\[ -6.29x - 49.4415 = -19.499 \]
-
Add \( 49.4415 \) to both sides to isolate the term with \( x \):
\[ -6.29x = -19.499 + 49.4415 \]
Calculate the right side:
\[ -19.499 + 49.4415 \approx 29.9425 \]
Now the equation is:
\[ -6.29x = 29.9425 \]
-
Divide both sides by \( -6.29 \) to solve for \( x \):
\[ x = \frac{29.9425}{-6.29} \]
Calculate that:
\[ x \approx -4.77 \]
Thus, the solution for \( x \) is approximately:
\[ \boxed{-4.77} \]