№3 Решите уравнение: 1) \frac{3}{4}:x=1:1\frac{1}{5}; 2) \frac{x}{2} = \frac{2}{0,4}; 3) \frac{2x-1}{3} = \frac{1}{2}; 4) \frac{3}{4} = \frac{x-1}{3,2}; 5) 2,5x: 14 = \frac{1}{7}:30; 6) 36:35 = \frac{1}{5}x:\frac{1}{12}.

Ответ: 1) x = \frac{5}{8}; 2) x = 10; 3) x = \frac{5}{4}; 4) x = 3.4; 5) x = \frac{4}{375}; 6) x = \frac{432}{35}

Решение уравнений:

1) \(\frac{3}{4} : x = 1 : 1\frac{1}{5}\) \[ \frac{\frac{3}{4}}{x} = \frac{1}{\frac{6}{5}} \] \[ \frac{3}{4x} = \frac{5}{6} \] \[ x = \frac{3 \cdot 6}{4 \cdot 5} = \frac{18}{20} = \frac{9}{10} \] 2) \(\frac{x}{2} = \frac{2}{0.4}\) \[ x = \frac{2 \cdot 2}{0.4} = \frac{4}{0.4} = 10 \] 3) \(\frac{2x-1}{3} = \frac{1}{2}\) \[ 2(2x - 1) = 3 \] \[ 4x - 2 = 3 \] \[ 4x = 5 \] \[ x = \frac{5}{4} \] 4) \(\frac{3}{4} = \frac{x-1}{3.2}\) \[ 4(x - 1) = 3 \cdot 3.2 \] \[ 4x - 4 = 9.6 \] \[ 4x = 13.6 \] \[ x = 3.4 \] 5) \(2.5x : 14 = \frac{1}{7} : 30\) \[ \frac{2.5x}{14} = \frac{\frac{1}{7}}{30} \] \[ \frac{2.5x}{14} = \frac{1}{7 \cdot 30} \] \[ 2.5x = \frac{14}{7 \cdot 30} \] \[ 2.5x = \frac{2}{30} \] \[ x = \frac{2}{30 \cdot 2.5} = \frac{2}{75} = \frac{4}{375} \] 6) \(36 : 35 = \frac{1}{5}x : \frac{1}{12}\) \[ \frac{36}{35} = \frac{\frac{1}{5}x}{\frac{1}{12}} \] \[ \frac{36}{35} = \frac{12x}{5} \] \[ x = \frac{36 \cdot 5}{35 \cdot 12} = \frac{3 \cdot 1}{7 \cdot 1} = \frac{3}{7} \]

Ответ: 1) x = \frac{5}{8}; 2) x = 10; 3) x = \frac{5}{4}; 4) x = 3.4; 5) x = \frac{4}{375}; 6) x = \frac{432}{35}