1. **State the problem:** Solve the equation $\frac{1}{2}(4g - 3) = 5g - 7$ for $g$. 2. **Use the distributive property:** Multiply both sides by 2 to eliminate the fraction. $$2 \times \frac{1}{2}(4g - 3) = 2 \times (5g - 7)$$ 3. **Simplify both sides:** $$\cancel{2} \times \frac{1}{\cancel{2}}(4g - 3) = 10g - 14$$ $$4g - 3 = 10g - 14$$ 4. **Isolate variable terms on one side:** Subtract $4g$ from both sides. $$4g - 3 - 4g = 10g - 14 - 4g$$ $$-3 = 6g - 14$$ 5. **Isolate constant terms:** Add 14 to both sides. $$-3 + 14 = 6g - 14 + 14$$ $$11 = 6g$$ 6. **Solve for $g$:** Divide both sides by 6. $$\frac{11}{\cancel{6}} = g \times \frac{1}{\cancel{6}}$$ $$g = \frac{11}{6}$$ **Final answer:** $g = \frac{11}{6}$