12. Решите уравнение: a) \( \frac{3}{7} - \left( x - \frac{1}{8} \right) = \frac{3}{4} - \frac{1}{2} \) б) \( \frac{2}{3} + \left( \frac{1}{8} + x \right) = \frac{5}{6} + \frac{1}{12} \) в) \( 3 - \left( x + 1\frac{1}{5} \right) = 1\frac{7}{25} \) г) \( 5 - \left( x + \frac{2}{3} \right) = 3\frac{5}{18} \) д) \( \left( \frac{5}{6}x - \frac{1}{4} \right) \cdot 16 = 6 \)\(\ne\)) \( \left( \frac{3}{5}x - \frac{2}{3} \right) \cdot 30 = 16 \) ж) \( \frac{3}{5}x - \frac{1}{3}x = 1\frac{4}{5} \) 3) \( \frac{3}{4}y - \frac{1}{3}y = 3\frac{1}{8} \)

Решение:

1. \( \frac{3}{7} - \left( x - \frac{1}{8} \right) = \frac{3}{4} - \frac{1}{2} \)
   \( \frac{3}{7} - \left( x - \frac{1}{8} \right) = \frac{3-2}{4} \)
   \( \frac{3}{7} - \left( x - \frac{1}{8} \right) = \frac{1}{4} \)
   \( x - \frac{1}{8} = \frac{3}{7} - \frac{1}{4} \)
   \( x - \frac{1}{8} = \frac{12-7}{28} \)
   \( x - \frac{1}{8} = \frac{5}{28} \)
   \( x = \frac{5}{28} + \frac{1}{8} \)
   \( x = \frac{10+7}{56} \)
   \( x = \frac{17}{56} \)
2. \( \frac{2}{3} + \left( \frac{1}{8} + x \right) = \frac{5}{6} + \frac{1}{12} \)
   \( \frac{2}{3} + \frac{1}{8} + x = \frac{10+1}{12} \)
   \( \frac{16+3}{24} + x = \frac{11}{12} \)
   \( \frac{19}{24} + x = \frac{11}{12} \)
   \( x = \frac{11}{12} - \frac{19}{24} \)
   \( x = \frac{22-19}{24} \)
   \( x = \frac{3}{24} \)
   \( x = \frac{1}{8} \)
3. \( 3 - \left( x + 1\frac{1}{5} \right) = 1\frac{7}{25} \)
   \( 3 - \left( x + \frac{6}{5} \right) = \frac{32}{25} \)
   \( x + \frac{6}{5} = 3 - \frac{32}{25} \)
   \( x + \frac{6}{5} = \frac{75-32}{25} \)
   \( x + \frac{6}{5} = \frac{43}{25} \)
   \( x = \frac{43}{25} - \frac{6}{5} \)
   \( x = \frac{43-30}{25} \)
   \( x = \frac{13}{25} \)
4. \( 5 - \left( x + \frac{2}{3} \right) = 3\frac{5}{18} \)
   \( 5 - \left( x + \frac{2}{3} \right) = \frac{54+5}{18} \)
   \( 5 - \left( x + \frac{2}{3} \right) = \frac{59}{18} \)
   \( x + \frac{2}{3} = 5 - \frac{59}{18} \)
   \( x + \frac{2}{3} = \frac{90-59}{18} \)
   \( x + \frac{2}{3} = \frac{31}{18} \)
   \( x = \frac{31}{18} - \frac{2}{3} \)
   \( x = \frac{31-12}{18} \)
   \( x = \frac{19}{18} \)
   \( x = 1\frac{1}{18} \)
5. \( \left( \frac{5}{6}x - \frac{1}{4} \right) \cdot 16 = 6 \)
   \( \frac{5}{6}x - \frac{1}{4} = \frac{6}{16} \)
   \( \frac{5}{6}x - \frac{1}{4} = \frac{3}{8} \)
   \( \frac{5}{6}x = \frac{3}{8} + \frac{1}{4} \)
   \( \frac{5}{6}x = \frac{3+2}{8} \)
   \( \frac{5}{6}x = \frac{5}{8} \)
   \( x = \frac{5}{8} : \frac{5}{6} \)
   \( x = \frac{5}{8} \cdot \frac{6}{5} \)
   \( x = \frac{6}{8} \)
   \( x = \frac{3}{4} \)
6. \( \left( \frac{3}{5}x - \frac{2}{3} \right) \cdot 30 = 16 \)
   \( \frac{3}{5}x - \frac{2}{3} = \frac{16}{30} \)
   \( \frac{3}{5}x - \frac{2}{3} = \frac{8}{15} \)
   \( \frac{3}{5}x = \frac{8}{15} + \frac{2}{3} \)
   \( \frac{3}{5}x = \frac{8+10}{15} \)
   \( \frac{3}{5}x = \frac{18}{15} \)
   \( x = \frac{18}{15} : \frac{3}{5} \)
   \( x = \frac{18}{15} \cdot \frac{5}{3} \)
   \( x = \frac{18 \cdot 5}{15 \cdot 3} = \frac{6 \cdot 5}{5 \cdot 3} = \frac{6}{3} \)
   \( x = 2 \)
7. \( \frac{3}{5}x - \frac{1}{3}x = 1\frac{4}{5} \)
   \( \frac{9-5}{15}x = \frac{9}{5} \)
   \( \frac{4}{15}x = \frac{9}{5} \)
   \( x = \frac{9}{5} : \frac{4}{15} \)
   \( x = \frac{9}{5} \cdot \frac{15}{4} \)
   \( x = \frac{9 \cdot 3}{4} \)
   \( x = \frac{27}{4} \)
   \( x = 6\frac{3}{4} \)
8. \( \frac{3}{4}y - \frac{1}{3}y = 3\frac{1}{8} \)
   \( \frac{9-4}{12}y = \frac{25}{8} \)
   \( \frac{5}{12}y = \frac{25}{8} \)
   \( y = \frac{25}{8} : \frac{5}{12} \)
   \( y = \frac{25}{8} \cdot \frac{12}{5} \)
   \( y = \frac{5 \cdot 3}{2} \)
   \( y = \frac{15}{2} \)
   \( y = 7\frac{1}{2} \)

Ответ: a) \( \frac{17}{56} \); б) \( \frac{1}{8} \); в) \( \frac{13}{25} \); г) \( 1\frac{1}{18} \); д) \( \frac{3}{4} \); е) 2; ж) \( 6\frac{3}{4} \); 3) \( 7\frac{1}{2} \).