To expand the expression \(-\frac{7}{6}(3g + 2)\) using the Distributive Property, we will distribute \(-\frac{7}{6}\) to both terms inside the parentheses:
- Distribute \(-\frac{7}{6}\) to \(3g\):
\[
-\frac{7}{6} \cdot 3g = -\frac{7 \cdot 3}{6}g = -\frac{21}{6}g = -\frac{7}{2}g \quad (\text{after simplifying} \frac{21}{6} \text{ to } \frac{7}{2} \text{ by dividing by 3})
\]
- Distribute \(-\frac{7}{6}\) to \(2\):
\[
-\frac{7}{6} \cdot 2 = -\frac{7 \cdot 2}{6} = -\frac{14}{6} = -\frac{7}{3} \quad (\text{after simplifying} \frac{14}{6} \text{ to } \frac{7}{3} \text{ by dividing by 2})
\]
- Combining these results gives:
\[
-\frac{7}{2}g - \frac{7}{3}
\]
Thus, the expanded expression is:
\(-\frac{7}{2}g - \frac{7}{3}\)