1. **Problem a:** Evaluate the expression $3(2x - 5) + \frac{x}{4}$ when $x = 8$. 2. **Step 1:** Substitute $x = 8$ into the expression: $$3(2 \times 8 - 5) + \frac{8}{4}$$ 3. **Step 2:** Simplify inside the parentheses: $$3(16 - 5) + 2$$ 4. **Step 3:** Calculate the subtraction: $$3 \times 11 + 2$$ 5. **Step 4:** Multiply: $$33 + 2$$ 6. **Step 5:** Add: $$35$$ --- 7. **Problem b:** Evaluate the expression $\frac{3 + 7q}{2} - \frac{4q - 1}{3}$ when $q = 7$. 8. **Step 1:** Substitute $q = 7$: $$\frac{3 + 7 \times 7}{2} - \frac{4 \times 7 - 1}{3}$$ 9. **Step 2:** Simplify inside the numerators: $$\frac{3 + 49}{2} - \frac{28 - 1}{3}$$ 10. **Step 3:** Calculate the sums and differences: $$\frac{52}{2} - \frac{27}{3}$$ 11. **Step 4:** Simplify the fractions: $$26 - 9$$ 12. **Step 5:** Subtract: $$17$$