20-18,6:\(6\frac{1}{5}-4\frac{3}{20}\) \(\frac{1}{6}\)x-982=\(\frac{3}{8}\)x-137 1\(\frac{5}{6}\):7\(\frac{1}{3}\)=1,6:x \(2\frac{7}{24}:1\frac{7}{15}-16,93\):1,1

Решение:

1. \( 20 - 18,6 : \left( 6\frac{1}{5} - 4\frac{3}{20} \right) \)
2. \( 6\frac{1}{5} - 4\frac{3}{20} = 6\frac{4}{20} - 4\frac{3}{20} = 2\frac{1}{20} = \frac{41}{20} \)
3. \( 20 - 18,6 : \frac{41}{20} = 20 - \frac{186}{10} \cdot \frac{20}{41} = 20 - \frac{93}{5} \cdot \frac{20}{41} = 20 - \frac{93 \cdot 4}{41} = 20 - \frac{372}{41} = \frac{820 - 372}{41} = \frac{448}{41} \)
4. \( \frac{1}{6}x - 982 = \frac{3}{8}x - 137 \)
5. \( \frac{1}{6}x - \frac{3}{8}x = 982 - 137 \)
6. \( \frac{4x - 9x}{24} = 845 \)
7. \( \frac{-5x}{24} = 845 \)
8. \( x = \frac{845 \cdot 24}{-5} = 169 \cdot (-24) = -4056 \)
9. \( 1\frac{5}{6} : 7\frac{1}{3} = 1,6 : x \)
10. \( 1\frac{5}{6} = \frac{11}{6} \)
11. \( 7\frac{1}{3} = \frac{22}{3} \)
12. \( \frac{11}{6} : \frac{22}{3} = \frac{11}{6} \cdot \frac{3}{22} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \)
13. \( \frac{1}{4} = 1,6 : x \)
14. \( x = 1,6 : \frac{1}{4} = 1,6 \cdot 4 = 6,4 \)
15. \( \left( 2\frac{7}{24} : 1\frac{7}{15} - 16,93 \right) : 1,1 \)
16. \( 2\frac{7}{24} = \frac{55}{24} \)
17. \( 1\frac{7}{15} = \frac{22}{15} \)
18. \( \frac{55}{24} : \frac{22}{15} = \frac{55}{24} \cdot \frac{15}{22} = \frac{5}{24} \cdot \frac{15}{2} = \frac{5 \cdot 5}{8 \cdot 2} = \frac{25}{16} = 1,5625 \)
19. \( 1,5625 - 16,93 = -15,3675 \)
20. \( -15,3675 : 1,1 = -13,97045... \)

Ответ:
1. \( \frac{448}{41} \)
2. \( x = -4056 \)
3. \( x = 6,4 \)
4. \( \approx -13,97 \)