1. **State the problem:** Solve the equation $$5x - (12 + x) = -13$$ and simplify the answer fully. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign: $$5x - 12 - x = -13$$ 3. **Combine like terms:** Combine the terms with $x$: $$5x - x = 4x$$ So the equation becomes: $$4x - 12 = -13$$ 4. **Isolate the variable term:** Add 12 to both sides to move constants to the right: $$4x = -13 + 12$$ $$4x = -1$$ 5. **Solve for $x$:** Divide both sides by 4: $$x = \frac{-1}{4}$$ 6. **Final answer:** The solution to the equation is: $$x = -\frac{1}{4}$$ This is fully reduced and simplified.