1. **State the problem:** Solve for $b$ in the equation $$2b - 7 = \frac{1}{3}b + 3$$. 2. **Isolate variable terms:** Subtract $\frac{1}{3}b$ from both sides to get all $b$ terms on one side: $$2b - \frac{1}{3}b - 7 = 3$$ 3. **Combine like terms:** Convert $2b$ to $\frac{6}{3}b$ to combine with $-\frac{1}{3}b$: $$\frac{6}{3}b - \frac{1}{3}b - 7 = 3$$ $$\frac{5}{3}b - 7 = 3$$ 4. **Isolate the term with $b$:** Add 7 to both sides: $$\frac{5}{3}b = 3 + 7$$ $$\frac{5}{3}b = 10$$ 5. **Solve for $b$:** Multiply both sides by the reciprocal of $\frac{5}{3}$ which is $\frac{3}{5}$: $$b = 10 \times \frac{3}{5}$$ $$b = 2 \times 3$$ $$b = 6$$ **Final answer:** $$b = 6$$