1. **State the problem:** We need to find the number of male adults who are not active members in a sports club in a district. 2. **Given data:** - 20% of adults are active members. - Of active members, 80% are women. - 20,000 adults are not active members. - The district has 1,000 more male adults than female adults. 3. **Define variables:** Let $W$ = number of adult women in the district. Let $M$ = number of adult men in the district. From the problem, we have: $$M = W + 1000$$ 4. **Total adults:** $$T = M + W = (W + 1000) + W = 2W + 1000$$ 5. **Active members:** 20% of $T$ are active members, so: $$A = 0.2T = 0.2(2W + 1000) = 0.4W + 200$$ 6. **Non-active members:** Given as 20,000, so: $$N = T - A = 20000$$ Substitute $T$ and $A$: $$ (2W + 1000) - (0.4W + 200) = 20000 $$ Simplify: $$ 2W + 1000 - 0.4W - 200 = 20000 $$ $$ (2W - 0.4W) + (1000 - 200) = 20000 $$ $$ 1.6W + 800 = 20000 $$ 7. **Solve for $W$:** $$ 1.6W = 20000 - 800 = 19200 $$ $$ W = \frac{19200}{1.6} $$ $$ W = 12000 $$ 8. **Find $M$:** $$ M = W + 1000 = 12000 + 1000 = 13000 $$ 9. **Active women:** 80% of active members are women: $$ A_w = 0.8A = 0.8(0.4W + 200) = 0.8(0.4 \times 12000 + 200) $$ $$ = 0.8(4800 + 200) = 0.8 \times 5000 = 4000 $$ 10. **Active men:** $$ A_m = A - A_w = (0.4W + 200) - 4000 = 5000 - 4000 = 1000 $$ 11. **Non-active men:** Total men minus active men: $$ N_m = M - A_m = 13000 - 1000 = 12000 $$ **Final answer:** There are $\boxed{12000}$ male adults who are not active members in a sports club in this district.