1. The problem is to solve the linear equation $$-2.5x - 4.8 = 7.7$$. 2. The goal is to isolate $x$ on one side of the equation. 3. First, add $4.8$ to both sides to cancel the $-4.8$ term: $$-2.5x - 4.8 + 4.8 = 7.7 + 4.8$$ which simplifies to $$-2.5x = 12.5$$ 4. Next, divide both sides by $-2.5$ to solve for $x$: $$\frac{-2.5x}{-2.5} = \frac{12.5}{-2.5}$$ showing the cancellation: $$\cancel{-2.5}x / \cancel{-2.5} = 12.5 / -2.5$$ 5. Simplify the right side: $$x = -5$$ 6. Therefore, the solution is $x = -5$. This method is correct and consistent with algebraic rules for solving linear equations.