1. **State the problem:** Factor the expression $$\frac{7}{2}a + 6$$ using $$\frac{1}{2}$$ as the common factor. 2. **Recall the factoring rule:** To factor out a common factor $$c$$ from terms $$x$$ and $$y$$, write $$x + y = c\left(\frac{x}{c} + \frac{y}{c}\right)$$. 3. **Apply the rule:** Here, $$c = \frac{1}{2}$$, so rewrite each term as a product of $$\frac{1}{2}$$ and another term: $$\frac{7}{2}a + 6 = \frac{1}{2} \left(\frac{\frac{7}{2}a}{\frac{1}{2}}\right) + \frac{1}{2} \left(\frac{6}{\frac{1}{2}}\right)$$ 4. **Simplify inside the parentheses:** $$\frac{\frac{7}{2}a}{\frac{1}{2}} = \frac{7}{2}a \times \frac{2}{1} = 7a$$ $$\frac{6}{\frac{1}{2}} = 6 \times 2 = 12$$ 5. **Write the factored form:** $$\frac{7}{2}a + 6 = \frac{1}{2}(7a) + \frac{1}{2}(12) = \frac{1}{2}(7a + 12)$$ **Final answer:** $$\boxed{\frac{1}{2}(7a + 12)}$$