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

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

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

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

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

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

$$x = 2$$

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

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

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

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

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

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

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

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

$$x = 4$$

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

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

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

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

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

$$x = \frac{2}{15} \cdot \frac{8}{1}$$

$$x = \frac{16}{15} = 1\frac{1}{15}$$

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

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

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

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

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

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

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

$$x = \frac{11}{3} \cdot \frac{1}{3}$$

$$x = \frac{11}{9} = 1\frac{2}{9}$$

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

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

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

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

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

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

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

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

$$x = \frac{1}{1} \cdot \frac{3}{4}$$

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

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

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

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

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

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

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

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

$$x = \frac{39}{1} \cdot \frac{1}{2}$$

$$x = \frac{39}{2} = 19\frac{1}{2}$$

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