609. Решите уравнение: a) 2/7 x = 2 2/7; б) 3/5 y = 2 9/10 - 1/5; в) 3/7 a + 2/5 = 1; г) 3 1/3 : k = 1 1/3 : 2; д) y : 1 1/2 = 2 1/3 * 1/3; е) 2/7 x + 3/7 x = 2 7/14; ж) m + 3/8 m = 1/4; з) y - 2/9 y = 4 2/3; и) 2/5 z + 2/3 z - 7/15 z = 2 1/2; к) 3 1/2 * (2/3 x + 4/7) = 2 1/3; л) (5/8 x - 1/5) * 3/4 = 3/4; м) 3/5 z + 2/3 z - 3 = 4/5.

609. Решите уравнение:

1. a) $$\frac{2}{7} x = 2\frac{2}{7}$$ $$\frac{2}{7} x = \frac{16}{7}$$ $$x = \frac{16}{7} : \frac{2}{7}$$ $$x = \frac{16}{7} \cdot \frac{7}{2}$$ $$x = 8$$

   Ответ: 8

2. б) $$\frac{3}{5} y = 2\frac{9}{10} - \frac{1}{5}$$ $$\frac{3}{5} y = \frac{29}{10} - \frac{2}{10}$$ $$\frac{3}{5} y = \frac{27}{10}$$ $$y = \frac{27}{10} : \frac{3}{5}$$ $$y = \frac{27}{10} \cdot \frac{5}{3}$$ $$y = \frac{9}{2} \cdot \frac{1}{1} = 4,5$$

   Ответ: 4,5

3. в) $$\frac{3}{7} a + \frac{2}{5} = 1$$ $$\frac{3}{7} a = 1 - \frac{2}{5}$$ $$\frac{3}{7} a = \frac{3}{5}$$ $$a = \frac{3}{5} : \frac{3}{7}$$ $$a = \frac{3}{5} \cdot \frac{7}{3}$$ $$a = \frac{7}{5} = 1,4$$

   Ответ: 1,4

4. г) $$3\frac{1}{3} : k = 1\frac{1}{3} : 2$$ $$\frac{10}{3} : k = \frac{4}{3} : 2$$ $$\frac{10}{3} : k = \frac{4}{3} \cdot \frac{1}{2} = \frac{2}{3}$$ $$k = \frac{10}{3} : \frac{2}{3}$$ $$k = \frac{10}{3} \cdot \frac{3}{2} = \frac{5}{1} \cdot \frac{1}{1} = 5$$

   Ответ: 5

5. д) $$y : 1\frac{1}{2} = 2\frac{1}{3} \cdot \frac{1}{3}$$ $$y : \frac{3}{2} = \frac{7}{3} \cdot \frac{1}{3} = \frac{7}{9}$$ $$y = \frac{7}{9} \cdot \frac{3}{2}$$ $$y = \frac{7}{3} \cdot \frac{1}{2} = \frac{7}{6} = 1\frac{1}{6}$$

   Ответ: $$1\frac{1}{6}$$

6. е) $$\frac{2}{7} x + \frac{3}{7} x = 2\frac{7}{14}$$ $$\frac{5}{7} x = 2\frac{1}{2}$$ $$\frac{5}{7} x = \frac{5}{2}$$ $$x = \frac{5}{2} : \frac{5}{7}$$ $$x = \frac{5}{2} \cdot \frac{7}{5}$$ $$x = \frac{1}{2} \cdot \frac{7}{1} = \frac{7}{2} = 3,5$$

   Ответ: 3,5

7. ж) $$m + \frac{3}{8} m = \frac{1}{4}$$ $$\frac{8}{8} m + \frac{3}{8} m = \frac{1}{4}$$ $$\frac{11}{8} m = \frac{1}{4}$$ $$m = \frac{1}{4} : \frac{11}{8}$$ $$m = \frac{1}{4} \cdot \frac{8}{11}$$ $$m = \frac{1}{1} \cdot \frac{2}{11} = \frac{2}{11}$$

   Ответ: 2/11

8. з) $$y - \frac{2}{9} y = 4\frac{2}{3}$$ $$\frac{9}{9} y - \frac{2}{9} y = \frac{14}{3}$$ $$\frac{7}{9} y = \frac{14}{3}$$ $$y = \frac{14}{3} : \frac{7}{9}$$ $$y = \frac{14}{3} \cdot \frac{9}{7}$$ $$y = \frac{2}{1} \cdot \frac{3}{1} = 6$$

   Ответ: 6

9. и) $$\frac{2}{5} z + \frac{2}{3} z - \frac{7}{15} z = 2\frac{1}{2}$$ $$\frac{6}{15} z + \frac{10}{15} z - \frac{7}{15} z = \frac{5}{2}$$ $$\frac{9}{15} z = \frac{5}{2}$$ $$\frac{3}{5} z = \frac{5}{2}$$ $$z = \frac{5}{2} : \frac{3}{5}$$ $$z = \frac{5}{2} \cdot \frac{5}{3} = \frac{25}{6} = 4\frac{1}{6}$$

   Ответ: $$4\frac{1}{6}$$

10. к) $$3\frac{1}{2} \cdot (\frac{2}{3} x + \frac{4}{7}) = 2\frac{1}{3}$$ $$\frac{7}{2} \cdot (\frac{2}{3} x + \frac{4}{7}) = \frac{7}{3}$$ $$\frac{2}{3} x + \frac{4}{7} = \frac{7}{3} : \frac{7}{2}$$ $$\frac{2}{3} x + \frac{4}{7} = \frac{7}{3} \cdot \frac{2}{7} = \frac{2}{3}$$ $$\frac{2}{3} x = \frac{2}{3} - \frac{4}{7}$$ $$\frac{2}{3} x = \frac{14}{21} - \frac{12}{21} = \frac{2}{21}$$ $$x = \frac{2}{21} : \frac{2}{3}$$ $$x = \frac{2}{21} \cdot \frac{3}{2} = \frac{1}{7} \cdot \frac{1}{1} = \frac{1}{7}$$

    Ответ: 1/7

11. л) $$(\frac{5}{8} x - \frac{1}{5}) \cdot \frac{3}{4} = \frac{3}{4}$$ $$\frac{5}{8} x - \frac{1}{5} = \frac{3}{4} : \frac{3}{4}$$ $$\frac{5}{8} x - \frac{1}{5} = 1$$ $$\frac{5}{8} x = 1 + \frac{1}{5} = \frac{6}{5}$$ $$x = \frac{6}{5} : \frac{5}{8}$$ $$x = \frac{6}{5} \cdot \frac{8}{5} = \frac{48}{25} = 1\frac{23}{25}$$

    Ответ: $$1\frac{23}{25}$$

12. м) $$\frac{3}{5} z + \frac{2}{3} z - 3 = \frac{4}{5}$$ $$\frac{9}{15} z + \frac{10}{15} z = \frac{4}{5} + 3$$ $$\frac{19}{15} z = \frac{4}{5} + \frac{15}{5} = \frac{19}{5}$$ $$z = \frac{19}{5} : \frac{19}{15}$$ $$z = \frac{19}{5} \cdot \frac{15}{19} = \frac{1}{1} \cdot \frac{3}{1} = 3$$

    Ответ: 3