1. **State the problem:** Solve for $a$ in the equation $$\frac{4}{7}a + 1 = 3$$. 2. **Isolate the term with $a$:** Subtract 1 from both sides: $$\frac{4}{7}a + 1 - 1 = 3 - 1$$ $$\frac{4}{7}a = 2$$ 3. **Solve for $a$:** Multiply both sides by the reciprocal of $\frac{4}{7}$, which is $\frac{7}{4}$: $$a = 2 \times \frac{7}{4}$$ 4. **Simplify:** $$a = \frac{2 \times 7}{4} = \frac{14}{4}$$ 5. **Reduce the fraction:** $$a = \frac{\cancel{14}^{7}}{\cancel{4}^{2}} = \frac{7}{2}$$ **Final answer:** $$a = \frac{7}{2}$$