1. **State the problem:** We need to solve the equation given by Kirchhoff's voltage law for the current $I$ in a series circuit: $$7.8I + 8.2I - 12.8 = 0$$ 2. **Combine like terms:** Add the terms with $I$: $$7.8I + 8.2I = (7.8 + 8.2)I = 16I$$ So the equation becomes: $$16I - 12.8 = 0$$ 3. **Isolate the term with $I$:** Add $12.8$ to both sides: $$16I - 12.8 + 12.8 = 0 + 12.8$$ $$16I = 12.8$$ 4. **Solve for $I$:** Divide both sides by $16$: $$I = \frac{12.8}{16}$$ Show cancellation: $$I = \frac{\cancel{12.8}}{\cancel{16}} = 0.8$$ 5. **Interpret the result:** The current $I$ is $0.8$ milliamps. **Final answer:** $$I = 0.8\text{ mA}$$