1. **State the problem:** Solve the equation $$7 + y = 5(2y - 1) + 3y$$ for $y$. 2. **Expand the right side:** Use the distributive property to expand $$5(2y - 1)$$. $$7 + y = 10y - 5 + 3y$$ 3. **Combine like terms on the right:** $$7 + y = 13y - 5$$ 4. **Isolate variable terms on one side:** Subtract $y$ from both sides. $$7 + \cancel{y} - \cancel{y} = 13y - 5 - y$$ $$7 = 12y - 5$$ 5. **Isolate constant terms on the other side:** Add 5 to both sides. $$7 + 5 = 12y - 5 + 5$$ $$12 = 12y$$ 6. **Solve for $y$:** Divide both sides by 12. $$\frac{12}{\cancel{12}} = \frac{12y}{\cancel{12}}$$ $$1 = y$$ **Final answer:** $$y = 1$$