1. **State the problem** Solve the inequality for $y$: $$10-\frac{5}{8}y>15$$ 2. **Write down the given inequality** $$10-\frac{5}{8}y>15$$ 3. **Subtract 10 from both sides** $$10-\frac{5}{8}y-10>15-10$$ $$-\frac{5}{8}y>5$$ 4. **Multiply both sides by the reciprocal of $-\frac{5}{8}$ (careful: flips the inequality)** We want to isolate $y$, so we divide by $-\frac{5}{8}$. $$-\frac{5}{8}y>5$$ $$\cancel{-\frac{5}{8}}\,y>\frac{5}{1}\quad\text{(show the canceled factor)}$$ $$y<\frac{5}{-\frac{5}{8}}$$ 5. **Simplify the fraction** $$y<\frac{5}{-\frac{5}{8}}=5\cdot\frac{8}{-5}$$ $$y<\frac{\cancel{5}\cdot 8}{-\cancel{5}}$$ $$y< -8$$ 6. **Final answer** The solution is $\boxed{y<-8}$.\n