1. **State the problem:** Solve the linear equation $-2.5x - 4.8 = 7.7$ for $x$. 2. **Isolate the variable term:** Add $4.8$ to both sides to move the constant term. $$-2.5x - 4.8 + 4.8 = 7.7 + 4.8$$ $$-2.5x = 12.5$$ 3. **Divide both sides by the coefficient of $x$ to solve for $x$:** $$x = \frac{12.5}{-2.5}$$ Show cancellation: $$x = \frac{\cancel{12.5}}{\cancel{-2.5}} \times \frac{5}{5} = \frac{12.5 \times 5}{-2.5 \times 5} = \frac{62.5}{-12.5}$$ Simplify: $$x = -5$$ 4. **Final answer:** $$\boxed{x = -5}$$