81. Решите уравнение: 1) x = 6/7 : 2/7 2) 8/11 - x = 1 3) 5/6 * x = 25 4) 6x = 1/4 5) x : 8/25 = 5/32 6) 4/7 : x = 2 2/35

Решение уравнений:

1. 1) \[ x = \frac{6}{7} : \frac{2}{7} \] \[ x = \frac{6}{7} \times \frac{7}{2} \] \[ x = \frac{6}{2} \] \[ x = 3 \]
2. 2) \[ \frac{8}{11} - x = 1 \] \[ x = \frac{8}{11} - 1 \] \[ x = \frac{8}{11} - \frac{11}{11} \] \[ x = \frac{8-11}{11} \] \[ x = -\frac{3}{11} \]
3. 3) \[ \frac{5}{6} \times x = 25 \] \[ x = 25 : \frac{5}{6} \] \[ x = 25 \times \frac{6}{5} \] \[ x = \frac{25 \times 6}{5} \] \[ x = 5 \times 6 \] \[ x = 30 \]
4. 4) \[ 6x = \frac{1}{4} \] \[ x = \frac{1}{4} : 6 \] \[ x = \frac{1}{4} \times \frac{1}{6} \] \[ x = \frac{1}{24} \]
5. 5) \[ x : \frac{8}{25} = \frac{5}{32} \] \[ x = \frac{5}{32} \times \frac{8}{25} \] \[ x = \frac{5 \times 8}{32 \times 25} \] \[ x = \frac{1 \times 1}{4 \times 5} \] \[ x = \frac{1}{20} \]
6. 6) \[ \frac{4}{7} : x = 2 \frac{2}{35} \] \[ \frac{4}{7} : x = \frac{2 \times 35 + 2}{35} \] \[ \frac{4}{7} : x = \frac{70 + 2}{35} \] \[ \frac{4}{7} : x = \frac{72}{35} \] \[ x = \frac{4}{7} : \frac{72}{35} \] \[ x = \frac{4}{7} \times \frac{35}{72} \] \[ x = \frac{4 \times 35}{7 \times 72} \] \[ x = \frac{1 \times 5}{1 \times 18} \] \[ x = \frac{5}{18} \]

Ответ: 1) 3; 2) -3/11; 3) 30; 4) 1/24; 5) 1/20; 6) 5/18