84. Найдите корень уравнения:

Решение:

1. \( \frac{6}{7} x = 2 \frac{1}{7} \)

\( \frac{6}{7} x = \frac{15}{7} \)

\( x = \frac{15}{7} : \frac{6}{7} = \frac{15}{7} \cdot \frac{7}{6} = \frac{15}{6} = \frac{5}{2} \)

2. \( \frac{8}{11} x = 1 \)

\( x = 1 : \frac{8}{11} = 1 \cdot \frac{11}{8} = \frac{11}{8} \)

3. \( \frac{5}{6} x = 25 \)

\( x = 25 : \frac{5}{6} = 25 \cdot \frac{6}{5} = 5 \cdot 6 = 30 \)

4. \( x : \frac{8}{25} = \frac{32}{30} \)

\( x = \frac{32}{30} \cdot \frac{8}{25} = \frac{16}{15} \cdot \frac{8}{25} = \frac{128}{375} \)

5. \( 4\frac{2}{7} : x = \frac{6}{35} \)

\( \frac{30}{7} : x = \frac{6}{35} \)

\( x = \frac{30}{7} : \frac{6}{35} = \frac{30}{7} \cdot \frac{35}{6} = 5 \cdot 5 = 25 \)

6. \( 3\frac{5}{7} : x = 1\frac{7}{9} \)

\( \frac{26}{7} : x = \frac{16}{9} \)

\( x = \frac{26}{7} : \frac{16}{9} = \frac{26}{7} \cdot \frac{9}{16} = \frac{13 \cdot 9}{7 \cdot 8} = \frac{117}{56} \)

Ответ: 1) \( \frac{5}{2} \); 2) \( \frac{11}{8} \); 3) 30; 4) \( \frac{128}{375} \); 5) 25; 6) \( \frac{117}{56} \).