85. Решите уравнение:

Решение:

1. \( \frac{1}{4} x + \frac{1}{6} x + \frac{5}{6} x = \frac{39}{56} \)

Приведём к общему знаменателю дроби в левой части. Общий знаменатель для 4 и 6 — 12.

\( \frac{3}{12} x + \frac{2}{12} x + \frac{10}{12} x = \frac{39}{56} \)

\( \frac{3+2+10}{12} x = \frac{39}{56} \)

\( \frac{15}{12} x = \frac{39}{56} \)

\( \frac{5}{4} x = \frac{39}{56} \)

\( x = \frac{39}{56} : \frac{5}{4} = \frac{39}{56} \cdot \frac{4}{5} = \frac{39 \cdot 4}{56 \cdot 5} = \frac{39 \cdot 1}{14 \cdot 5} = \frac{39}{70} \)

2. \( 2\frac{2}{3} x - 1\frac{5}{7} = 3\frac{1}{21} \)

\( \frac{8}{3} x - \frac{12}{7} = \frac{64}{21} \)

\( \frac{8}{3} x = \frac{64}{21} + \frac{12}{7} \)

\( \frac{8}{3} x = \frac{64}{21} + \frac{12 \cdot 3}{7 \cdot 3} = \frac{64}{21} + \frac{36}{21} \)

\( \frac{8}{3} x = \frac{64+36}{21} = \frac{100}{21} \)

\( x = \frac{100}{21} : \frac{8}{3} = \frac{100}{21} \cdot \frac{3}{8} = \frac{100 \cdot 3}{21 \cdot 8} = \frac{25 \cdot 1}{7 \cdot 2} = \frac{25}{14} \)

3. \( 3\frac{3}{14} - \frac{1}{7} x = 1\frac{2}{7} \)

\( \frac{45}{14} - \frac{1}{7} x = \frac{9}{7} \)

\( \frac{1}{7} x = \frac{45}{14} - \frac{9}{7} \)

\( \frac{1}{7} x = \frac{45}{14} - \frac{9 \cdot 2}{7 \cdot 2} = \frac{45}{14} - \frac{18}{14} \)

\( \frac{1}{7} x = \frac{45-18}{14} = \frac{27}{14} \)

\( x = \frac{27}{14} : \frac{1}{7} = \frac{27}{14} \cdot 7 = \frac{27}{2} \)

4. \( 5x + 2\frac{1}{2} = 6\frac{1}{4} \)

\( 5x + \frac{5}{2} = \frac{25}{4} \)

\( 5x = \frac{25}{4} - \frac{5}{2} = \frac{25}{4} - \frac{10}{4} = \frac{15}{4} \)

\( x = \frac{15}{4} : 5 = \frac{15}{4} \cdot \frac{1}{5} = \frac{3}{4} \)

Ответ: 1) \( \frac{39}{70} \); 2) \( \frac{25}{14} \); 3) \( \frac{27}{2} \); 4) \( \frac{3}{4} \).