3 Решите уравнение: 1) 4\frac{5}{7}(x-6\frac{3}{7})=2\frac{6}{7}; 2) 19\frac{28}{34}-(m+2\frac{20}{34})=12\frac{15}{34}; 3) 32-x=9\frac{18}{35}.

Решение:

1. $$4\frac{5}{7}(x-6\frac{3}{7})=2\frac{6}{7}$$ $$\frac{33}{7}(x-\frac{45}{7}) = \frac{20}{7}$$ $$x-\frac{45}{7} = \frac{20}{7} : \frac{33}{7} = \frac{20}{7} \cdot \frac{7}{33} = \frac{20}{33}$$ $$x = \frac{20}{33} + \frac{45}{7}$$ $$x = \frac{20 \cdot 7 + 45 \cdot 33}{33 \cdot 7} = \frac{140 + 1485}{231} = \frac{1625}{231} = 7\frac{8}{231}$$
2. $$19\frac{28}{34}-(m+2\frac{20}{34})=12\frac{15}{34}$$ $$m+2\frac{20}{34} = 19\frac{28}{34} - 12\frac{15}{34}$$ $$m + 2\frac{20}{34} = (19-12) + (\frac{28}{34} - \frac{15}{34}) = 7 + \frac{13}{34} = 7\frac{13}{34}$$ $$m = 7\frac{13}{34} - 2\frac{20}{34} = (7-2) + (\frac{13}{34} - \frac{20}{34}) = 5 - \frac{7}{34} = 4\frac{34}{34} - \frac{7}{34} = 4\frac{27}{34}$$
3. $$32-x=9\frac{18}{35}$$ $$x=32-9\frac{18}{35}$$ $$x = 32-9 - \frac{18}{35} = 23 - \frac{18}{35} = 22\frac{35}{35} - \frac{18}{35} = 22\frac{17}{35}$$

Ответ: 1) $$7\frac{8}{231}$$; 2) $$4\frac{27}{34}$$; 3) $$22\frac{17}{35}$$.