Вариант 5: Решите уравнение: a) 8/25 * x = 3/5 б) 7/12 * y = 1 1/4 в) y - 7/12 = 4 1/6 г) (7/12 + 11/30) : x = 1 1/4 : 3 1/3 д) 3/15 - 1 1/14 * x = 1/6 е) (7,1y - y) : 0,6 = 3,05

Вариант 5. Решение:

Решите уравнение:

1. a) \( \frac{8}{25} x = \frac{3}{5} \)
   \( x = \frac{3}{5} : \frac{8}{25} = \frac{3}{5} \cdot \frac{25}{8} = \frac{3 \cdot 5}{8} = \frac{15}{8} = 1\frac{7}{8} \)
2. б) \( \frac{7}{12} y = 1\frac{1}{4} \)
   \( y = 1\frac{1}{4} : \frac{7}{12} = \frac{5}{4} : \frac{7}{12} = \frac{5}{4} \cdot \frac{12}{7} = \frac{5 \cdot 3}{7} = \frac{15}{7} = 2\frac{1}{7} \)
3. в) \( y - \frac{7}{12} = 4\frac{1}{6} \)
   \( y = 4\frac{1}{6} + \frac{7}{12} = \frac{25}{6} + \frac{7}{12} = \frac{50}{12} + \frac{7}{12} = \frac{57}{12} = \frac{19}{4} = 4\frac{3}{4} \)
4. г) \( \left( \frac{7}{12} + \frac{11}{30} \right) : x = 1\frac{1}{4} : 3\frac{1}{3} \)
   \( \frac{7 \cdot 5 + 11 \cdot 2}{60} : x = \frac{5}{4} : \frac{10}{3} \)
   \( \frac{35 + 22}{60} : x = \frac{5}{4} \cdot \frac{3}{10} \)
   \( \frac{57}{60} : x = \frac{15}{40} \)
   \( \frac{19}{20} : x = \frac{3}{8} \)
   \( x = \frac{19}{20} : \frac{3}{8} = \frac{19}{20} \cdot \frac{8}{3} = \frac{19 \cdot 2}{5 \cdot 3} = \frac{38}{15} = 2\frac{8}{15} \)
5. д) \( \frac{3}{15} - 1\frac{1}{14} x = \frac{1}{6} \)
   \( \frac{1}{5} - \frac{15}{14} x = \frac{1}{6} \)
   \( -\frac{15}{14} x = \frac{1}{6} - \frac{1}{5} \)
   \( -\frac{15}{14} x = \frac{5 - 6}{30} \)
   \( -\frac{15}{14} x = -\frac{1}{30} \)
   \( x = \frac{1}{30} : \frac{15}{14} = \frac{1}{30} \cdot \frac{14}{15} = \frac{1 \cdot 7}{15 \cdot 15} = \frac{7}{225} \)
6. е) \( (7,1y - y) : 0,6 = 3,05 \)
   \( 6,1y : 0,6 = 3,05 \)
   \( 6,1y = 3,05 \cdot 0,6 \)
   \( 6,1y = 1,83 \)
   \( y = 1,83 : 6,1 = 0,3 \)

Ответ: а) 15/8; б) 15/7; в) 19/4; г) 38/15; д) 7/225; е) 0,3.