5. Решите уравнение: 1) $$x-7\frac{1}{3}=12\frac{5}{12}$$; 2) $$(5\frac{7}{9}-x)+2\frac{3}{4}=3\frac{5}{12}$$.

1. $$x-7\frac{1}{3}=12\frac{5}{12}$$ $$x = 12\frac{5}{12}+7\frac{1}{3}$$ $$x = \frac{149}{12} + \frac{22}{3} = \frac{149}{12} + \frac{22 \cdot 4}{3 \cdot 4} = \frac{149}{12} + \frac{88}{12} = \frac{237}{12} = 19\frac{9}{12} = 19\frac{3}{4}$$
2. $$(5\frac{7}{9}-x)+2\frac{3}{4}=3\frac{5}{12}$$ $$5\frac{7}{9}-x = 3\frac{5}{12}-2\frac{3}{4}$$ $$5\frac{7}{9}-x = \frac{41}{12} - \frac{11}{4} = \frac{41}{12} - \frac{11 \cdot 3}{4 \cdot 3} = \frac{41}{12} - \frac{33}{12} = \frac{8}{12} = \frac{2}{3}$$ $$x = 5\frac{7}{9} - \frac{2}{3} = \frac{52}{9} - \frac{2}{3} = \frac{52}{9} - \frac{2 \cdot 3}{3 \cdot 3} = \frac{52}{9} - \frac{6}{9} = \frac{46}{9} = 5\frac{1}{9}$$

Ответ:

1. $$x = 19\frac{3}{4}$$
2. $$x = 5\frac{1}{9}$$