1. **State the problem:** Solve for $k$ in the equation $$3(k + 1) + 1 = 7$$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses. $$3(k + 1) = 3k + 3$$ So the equation becomes: $$3k + 3 + 1 = 7$$ 3. **Combine like terms:** $$3k + 4 = 7$$ 4. **Isolate the term with $k$:** Subtract 4 from both sides. $$3k + \cancel{4} - \cancel{4} = 7 - 4$$ $$3k = 3$$ 5. **Solve for $k$:** Divide both sides by 3. $$\frac{3k}{\cancel{3}} = \frac{3}{\cancel{3}}$$ $$k = 1$$ **Final answer:** $$k = 1$$