1. **State the problem:** Solve the equation $$\frac{5(2w + 1)}{3} = 11$$ for $w$. 2. **Understand the formula and rules:** This is a linear equation with a fraction. To solve, we first eliminate the denominator by multiplying both sides by 3. 3. **Multiply both sides by 3:** $$\cancel{3} \times \frac{5(2w + 1)}{\cancel{3}} = 11 \times 3$$ which simplifies to $$5(2w + 1) = 33$$ 4. **Distribute 5 inside the parentheses:** $$5 \times 2w + 5 \times 1 = 33$$ $$10w + 5 = 33$$ 5. **Subtract 5 from both sides:** $$10w + \cancel{5} - \cancel{5} = 33 - 5$$ $$10w = 28$$ 6. **Divide both sides by 10:** $$\frac{\cancel{10}w}{\cancel{10}} = \frac{28}{10}$$ $$w = \frac{28}{10}$$ 7. **Simplify the fraction:** $$w = \frac{14}{5}$$ **Final answer:** $$w = \frac{14}{5}$$