84. Решите уравнение:

Решение:

1. \( \frac{1}{2} x + \frac{1}{3} x + \frac{1}{4} x = \frac{26}{27} \implies \left( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} \right) x = \frac{26}{27} \implies \left( \frac{6+4+3}{12} \right) x = \frac{26}{27} \implies \frac{13}{12} x = \frac{26}{27} \implies x = \frac{26}{27} \cdot \frac{12}{13} = \frac{2 \cdot 4}{9} = \frac{8}{9} \)
2. \( 2 \frac{2}{3} x - 2 \frac{5}{6} = 1 \frac{7}{15} \implies \frac{8}{3} x - \frac{17}{6} = \frac{22}{15} \implies \frac{8}{3} x = \frac{22}{15} + \frac{17}{6} = \frac{44+85}{30} = \frac{129}{30} = \frac{43}{10} \implies x = \frac{43}{10} \cdot \frac{3}{8} = \frac{129}{80} \)
3. \( 4 \frac{1}{12} - 5 \frac{3}{5} x = 2 \frac{2}{3} \implies \frac{49}{12} - \frac{28}{5} x = \frac{8}{3} \implies -\frac{28}{5} x = \frac{8}{3} - \frac{49}{12} = \frac{32-49}{12} = -\frac{17}{12} \implies x = -\frac{17}{12} \cdot \left( -\frac{5}{28} \right) = \frac{85}{336} \)
4. \( x + 2 \frac{1}{2} = 10 \frac{5}{6} \implies x = 10 \frac{5}{6} - 2 \frac{1}{2} = \frac{65}{6} - \frac{5}{2} = \frac{65-15}{6} = \frac{50}{6} = \frac{25}{3} \)

Ответ: 1) \( x = \frac{8}{9} \); 2) \( x = \frac{129}{80} \); 3) \( x = \frac{85}{336} \); 4) \( x = \frac{25}{3} \).