1. **State the problem:** Solve the equation $-3y + 7 - 4 = 2y - 5 + 3y$ for $y$. 2. **Simplify both sides:** Left side: $7 - 4 = 3$, so the left side becomes $-3y + 3$. Right side: $2y + 3y = 5y$, so the right side becomes $5y - 5$. 3. **Rewrite the equation:** $$-3y + 3 = 5y - 5$$ 4. **Isolate variable terms on one side:** Add $3y$ to both sides: $$3 = 5y - 5 + 3y$$ $$3 = 8y - 5$$ 5. **Isolate constant terms on the other side:** Add $5$ to both sides: $$3 + 5 = 8y$$ $$8 = 8y$$ 6. **Solve for $y$:** Divide both sides by $8$: $$y = \frac{8}{8} = 1$$ **Final answer:** $$y = 1$$