1. **State the problem:** Solve the equation $$7 = \frac{b}{3} - 5b + 2$$ for $b$. 2. **Rewrite the equation:** Move all terms to one side to isolate $b$ terms. $$7 = \frac{b}{3} - 5b + 2$$ 3. **Subtract 2 from both sides:** $$7 - 2 = \frac{b}{3} - 5b$$ $$5 = \frac{b}{3} - 5b$$ 4. **Express $-5b$ as $-\frac{15b}{3}$ to have a common denominator:** $$5 = \frac{b}{3} - \frac{15b}{3}$$ 5. **Combine the fractions:** $$5 = \frac{b - 15b}{3} = \frac{-14b}{3}$$ 6. **Multiply both sides by 3 to eliminate the denominator:** $$3 \times 5 = 3 \times \frac{-14b}{3}$$ $$15 = \cancel{3} \times \frac{-14b}{\cancel{3}}$$ $$15 = -14b$$ 7. **Divide both sides by -14 to solve for $b$:** $$b = \frac{15}{-14} = -\frac{15}{14}$$ **Final answer:** $$b = -\frac{15}{14}$$