418 Реши уравнения: 1) (3,6-2,5x)·1$$\frac{5}{7}$$-$$\frac{5}{7}$$= 1,6; 2) $$\frac{2}{3}$$y + 2y + $$\frac{5}{6}$$y + 1,5y = 0,35; 3) 9z-14 = 7z +8; 4) $$\frac{1,6}{n+6}$$ = $$\frac{3}{5n}$$

1) Решим уравнение: $$(3,6 - 2,5x) \cdot 1\frac{5}{7} - \frac{5}{7} = 1,6$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} - \frac{5}{7} = 1,6$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = 1,6 + \frac{5}{7}$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = \frac{16}{10} + \frac{5}{7}$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = \frac{8}{5} + \frac{5}{7}$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = \frac{8 \cdot 7 + 5 \cdot 5}{35}$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = \frac{56 + 25}{35}$$ $$(3,6 - 2,5x) \cdot \frac{12}{7} = \frac{81}{35}$$ $$3,6 - 2,5x = \frac{81}{35} : \frac{12}{7}$$ $$3,6 - 2,5x = \frac{81}{35} \cdot \frac{7}{12}$$ $$3,6 - 2,5x = \frac{81}{5 \cdot 12}$$ $$3,6 - 2,5x = \frac{27}{5 \cdot 4}$$ $$3,6 - 2,5x = \frac{27}{20}$$ $$3,6 - 2,5x = 1,35$$ $$2,5x = 3,6 - 1,35$$ $$2,5x = 2,25$$ $$x = 2,25 : 2,5$$ $$x = 225 : 250$$ $$x = 9 : 10$$ $$x = 0,9$$ Ответ: x = 0,9 2) Решим уравнение: $$\frac{2}{3}y + 2y + \frac{5}{6}y + 1,5y = 0,35$$ $$\frac{2}{3}y + 2y + \frac{5}{6}y + \frac{3}{2}y = \frac{35}{100}$$ $$\frac{2}{3}y + \frac{2}{1}y + \frac{5}{6}y + \frac{3}{2}y = \frac{7}{20}$$ $$\frac{2 \cdot 2}{3 \cdot 2}y + \frac{2 \cdot 6}{1 \cdot 6}y + \frac{5}{6}y + \frac{3 \cdot 3}{2 \cdot 3}y = \frac{7}{20}$$ $$\frac{4}{6}y + \frac{12}{6}y + \frac{5}{6}y + \frac{9}{6}y = \frac{7}{20}$$ $$\frac{4+12+5+9}{6}y = \frac{7}{20}$$ $$\frac{30}{6}y = \frac{7}{20}$$ $$5y = \frac{7}{20}$$ $$y = \frac{7}{20} : 5$$ $$y = \frac{7}{20} : \frac{5}{1}$$ $$y = \frac{7}{20} \cdot \frac{1}{5}$$ $$y = \frac{7}{100}$$ $$y = 0,07$$ Ответ: y = 0,07 3) Решим уравнение: $$9z - 14 = 7z + 8$$ $$9z - 7z = 8 + 14$$ $$2z = 22$$ $$z = 11$$ Ответ: z = 11 4) Решим уравнение: $$\frac{1,6}{n+6} = \frac{3}{5n}$$ $$1,6 \cdot 5n = 3 \cdot (n+6)$$ $$8n = 3n + 18$$ $$8n - 3n = 18$$ $$5n = 18$$ $$n = \frac{18}{5}$$ $$n = 3,6$$ Ответ: n = 3,6