4. Решите уравнение: 1) x - \frac{3}{14}x = 1 \frac{4}{7}; 2) \frac{11}{18}x + \frac{1}{3} = 2 \frac{7}{9}; 3) \frac{1}{3}x + \frac{1}{4}x + \frac{1}{8}x = \frac{34}{45}; 4) 3 \frac{3}{4}x - 1 \frac{2}{3} = 2 \frac{11}{12}; 5) 4 \frac{2}{15} - 3 \frac{1}{9}x = 1 \frac{4}{5}; 6) \frac{4}{15}x + 2 \frac{1}{3} = 7 \frac{8}{15}.

1) $$x - \frac{3}{14}x = 1 \frac{4}{7};$$

$$x(1 - \frac{3}{14}) = \frac{11}{7};$$

$$x(\frac{14}{14} - \frac{3}{14}) = \frac{11}{7};$$

$$x(\frac{11}{14}) = \frac{11}{7};$$

$$x = \frac{11}{7} : \frac{11}{14};$$

$$x = \frac{11}{7} \cdot \frac{14}{11};$$

$$x = 2$$

2) $$\frac{11}{18}x + \frac{1}{3} = 2 \frac{7}{9};$$

$$\frac{11}{18}x = \frac{25}{9} - \frac{1}{3};$$

$$\frac{11}{18}x = \frac{25}{9} - \frac{3}{9};$$

$$\frac{11}{18}x = \frac{22}{9};$$

$$x = \frac{22}{9} : \frac{11}{18};$$

$$x = \frac{22}{9} \cdot \frac{18}{11};$$

$$x = 4$$

3) $$\frac{1}{3}x + \frac{1}{4}x + \frac{1}{8}x = \frac{34}{45};$$

$$x(\frac{1}{3} + \frac{1}{4} + \frac{1}{8}) = \frac{34}{45};$$

$$x(\frac{8}{24} + \frac{6}{24} + \frac{3}{24}) = \frac{34}{45};$$

$$x(\frac{17}{24}) = \frac{34}{45};$$

$$x = \frac{34}{45} : \frac{17}{24};$$

$$x = \frac{34}{45} \cdot \frac{24}{17};$$

$$x = \frac{16}{15}$$

$$x = 1 \frac{1}{15}$$

4) $$3 \frac{3}{4}x - 1 \frac{2}{3} = 2 \frac{11}{12};$$

$$\frac{15}{4}x - \frac{5}{3} = \frac{35}{12};$$

$$\frac{15}{4}x = \frac{35}{12} + \frac{5}{3};$$

$$\frac{15}{4}x = \frac{35}{12} + \frac{20}{12};$$

$$\frac{15}{4}x = \frac{55}{12};$$

$$x = \frac{55}{12} : \frac{15}{4};$$

$$x = \frac{55}{12} \cdot \frac{4}{15};$$

$$x = \frac{11}{9}$$

$$x = 1 \frac{2}{9}$$

5) $$4 \frac{2}{15} - 3 \frac{1}{9}x = 1 \frac{4}{5};$$

$$\frac{62}{15} - \frac{28}{9}x = \frac{9}{5};$$

$$\frac{28}{9}x = \frac{62}{15} - \frac{9}{5};$$

$$\frac{28}{9}x = \frac{62}{15} - \frac{27}{15};$$

$$\frac{28}{9}x = \frac{35}{15};$$

$$\frac{28}{9}x = \frac{7}{3};$$

$$x = \frac{7}{3} : \frac{28}{9};$$

$$x = \frac{7}{3} \cdot \frac{9}{28};$$

$$x = \frac{3}{4}$$

6) $$\frac{4}{15}x + 2 \frac{1}{3} = 7 \frac{8}{15};$$

$$\frac{4}{15}x + \frac{7}{3} = \frac{113}{15};$$

$$\frac{4}{15}x = \frac{113}{15} - \frac{7}{3};$$

$$\frac{4}{15}x = \frac{113}{15} - \frac{35}{15};$$

$$\frac{4}{15}x = \frac{78}{15};$$

$$x = \frac{78}{15} : \frac{4}{15};$$

$$x = \frac{78}{15} \cdot \frac{15}{4};$$

$$x = \frac{39}{2}$$

$$x = 19 \frac{1}{2}$$

Ответ: 1) 2; 2) 4; 3) 1 \frac{1}{15}; 4) 1 \frac{2}{9}; 5) \frac{3}{4}; 6) 19 \frac{1}{2}