1. **State the problem:** Solve the equation $$6 - 2(a + 1) = 7 + a$$ for the variable $a$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses. $$6 - 2a - 2 = 7 + a$$ 3. **Simplify the left side:** Combine like terms. $$6 - 2 = 4$$ So the equation becomes: $$4 - 2a = 7 + a$$ 4. **Get all terms with $a$ on one side:** Add $2a$ to both sides to move $-2a$ to the right. $$4 - \cancel{2a} + 2a = 7 + a + 2a$$ Simplifies to: $$4 = 7 + 3a$$ 5. **Isolate the term with $a$:** Subtract $7$ from both sides. $$4 - 7 = 7 - \cancel{7} + 3a$$ Simplifies to: $$-3 = 3a$$ 6. **Solve for $a$:** Divide both sides by $3$. $$\frac{-3}{\cancel{3}} = \frac{3a}{\cancel{3}}$$ Simplifies to: $$-1 = a$$ 7. **Final answer:** $$a = -1$$