3. Решите уравнение: 1) 6/7 * x = 2/7; 2) 8/11 * x = 1; 3) 5/6 * x = 25; 4) 6x = 1/4; 5) x : 8/25 = 5/32; 6) 20/63 : x = 4/7.

Решение:

• 1) \( \frac{6}{7}x = \frac{2}{7} \Rightarrow x = \frac{2}{7} : \frac{6}{7} = \frac{2}{7} \times \frac{7}{6} = \frac{2}{6} = \frac{1}{3} \)
• 2) \( \frac{8}{11}x = 1 \Rightarrow x = 1 : \frac{8}{11} = 1 \times \frac{11}{8} = \frac{11}{8} \)
• 3) \( \frac{5}{6}x = 25 \Rightarrow x = 25 : \frac{5}{6} = 25 \times \frac{6}{5} = 5 \times 6 = 30 \)
• 4) \( 6x = \frac{1}{4} \Rightarrow x = \frac{1}{4} : 6 = \frac{1}{4} \times \frac{1}{6} = \frac{1}{24} \)
• 5) \( x : \frac{8}{25} = \frac{5}{32} \Rightarrow x = \frac{5}{32} \times \frac{8}{25} = \frac{5 \times 8}{32 \times 25} = \frac{1 \times 1}{4 \times 5} = \frac{1}{20} \)
• 6) \( \frac{20}{63} : x = \frac{4}{7} \Rightarrow x = \frac{20}{63} : \frac{4}{7} = \frac{20}{63} \times \frac{7}{4} = \frac{20 \times 7}{63 \times 4} = \frac{5 \times 1}{9 \times 1} = \frac{5}{9} \)

Ответ: 1) \( \frac{1}{3} \) 2) \( \frac{11}{8} \) 3) 30 4) \( \frac{1}{24} \) 5) \( \frac{1}{20} \) 6) \( \frac{5}{9} \)