1. **Problem 1:** Solve the equation $2 - 16 = -32 - \frac{2}{5}f$. 2. First, simplify the left side: $2 - 16 = -14$. 3. Rewrite the equation: $-14 = -32 - \frac{2}{5}f$. 4. Add 32 to both sides to isolate the term with $f$: $$-14 + 32 = -32 + 32 - \frac{2}{5}f$$ $$18 = - \frac{2}{5}f$$ 5. To solve for $f$, multiply both sides by the reciprocal of $-\frac{2}{5}$, which is $-\frac{5}{2}$: $$f = 18 \times -\frac{5}{2}$$ 6. Calculate: $$f = 18 \times -\frac{5}{2} = -45$$ --- 7. **Problem 2:** Solve the equation $4 \times \frac{2}{3}x - 7 = 8$. 8. First, multiply $4$ by $\frac{2}{3}$: $$4 \times \frac{2}{3}x = \frac{8}{3}x$$ 9. Rewrite the equation: $$\frac{8}{3}x - 7 = 8$$ 10. Add 7 to both sides: $$\frac{8}{3}x - 7 + 7 = 8 + 7$$ $$\frac{8}{3}x = 15$$ 11. Multiply both sides by the reciprocal of $\frac{8}{3}$, which is $\frac{3}{8}$: $$x = 15 \times \frac{3}{8}$$ 12. Calculate: $$x = \frac{45}{8} = 5.625$$