463. Решите уравнение: 5) 2 1/3 x - 1 1/6 = 1 5/9; 6) 2 1/9 : (x - 1 1/6) = 1 5/9; 7) 27 : (3 1/7 - 2 11/14) x = 1 1/8; 8) 48 : (3 4/5 x - 25) = 1 1/2.

Решение:

1. \( 2 \frac{1}{3} x - 1 \frac{1}{6} = 1 \frac{5}{9} \Rightarrow \frac{7}{3} x = 1 \frac{5}{9} + 1 \frac{1}{6} = \frac{14}{9} + \frac{7}{6} = \frac{28 + 21}{18} = \frac{49}{18} \Rightarrow x = \frac{49}{18} \times \frac{3}{7} = \frac{7}{6} = 1 \frac{1}{6} \)
2. \( 2 \frac{1}{9} : (x - 1 \frac{1}{6}) = 1 \frac{5}{9} \Rightarrow \frac{19}{9} : (x - \frac{7}{6}) = \frac{14}{9} \Rightarrow x - \frac{7}{6} = \frac{19}{9} \times \frac{9}{14} = \frac{19}{14} \Rightarrow x = \frac{19}{14} + \frac{7}{6} = \frac{57 + 49}{42} = \frac{106}{42} = \frac{53}{21} = 2 \frac{11}{21} \)
3. \( 27 : (3 \frac{1}{7} - 2 \frac{11}{14}) x = 1 \frac{1}{8} \Rightarrow 27 : (\frac{22}{7} - \frac{39}{14}) x = \frac{9}{8} \Rightarrow 27 : (\frac{44 - 39}{14}) x = \frac{9}{8} \Rightarrow 27 : \frac{5}{14} x = \frac{9}{8} \Rightarrow \frac{27 \times 14}{5} x = \frac{9}{8} \Rightarrow \frac{378}{5} x = \frac{9}{8} \Rightarrow x = \frac{9}{8} \times \frac{5}{378} = \frac{1}{8} \times \frac{5}{42} = \frac{5}{336} \)
4. \( 48 : (3 \frac{4}{5} x - 25) = 1 \frac{1}{2} \Rightarrow 48 : (\frac{3x}{5} - 25) = \frac{3}{2} \Rightarrow \frac{3x}{5} - 25 = 48 \times \frac{2}{3} = 32 \Rightarrow \frac{3x}{5} = 32 + 25 = 57 \Rightarrow x = 57 \times \frac{5}{3} = 19 \times 5 = 95 \)

Ответ: 5) \(x = 1 \frac{1}{6}\); 6) \(x = 2 \frac{11}{21}\); 7) \(x = \frac{5}{336}\); 8) \(x = 95\).