4. Решите уравнение: 1) x- 2/15x = 1 3/5; 2) 7/12x + 1/4 = 3 5/6; 3) 1/4x + 1/5x + 1/10x = 39/70; 4) 2 2/3x - 1 1/4 = 3 5/6; 5) 5 1/6 - 2 1/8x = 1 3/4; 6) 3/10x + 1 2/5 = 6 1/2.

4. Решите уравнение:

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

$$\frac{15}{15}x - \frac{2}{15}x = \frac{8}{5}$$

$$\frac{13}{15}x = \frac{8}{5}$$

$$x = \frac{8}{5} : \frac{13}{15}$$

$$x = \frac{8}{5} \cdot \frac{15}{13}$$

$$x = \frac{8 \cdot 15}{5 \cdot 13}$$

$$x = \frac{8 \cdot 3}{1 \cdot 13}$$

$$x = \frac{24}{13} = 1\frac{11}{13}$$

Ответ: $$x = 1\frac{11}{13}$$

2) $$\frac{7}{12}x + \frac{1}{4} = 3 \frac{5}{6}$$

$$\frac{7}{12}x = \frac{23}{6} - \frac{1}{4}$$

$$\frac{7}{12}x = \frac{23 \cdot 2 - 1 \cdot 3}{12}$$

$$\frac{7}{12}x = \frac{46 - 3}{12}$$

$$\frac{7}{12}x = \frac{43}{12}$$

$$x = \frac{43}{12} : \frac{7}{12}$$

$$x = \frac{43}{12} \cdot \frac{12}{7}$$

$$x = \frac{43}{7} = 6 \frac{1}{7}$$

Ответ: $$x = 6 \frac{1}{7}$$

3) $$\frac{1}{4}x + \frac{1}{5}x + \frac{1}{10}x = \frac{39}{70}$$

$$\frac{5}{20}x + \frac{4}{20}x + \frac{2}{20}x = \frac{39}{70}$$

$$\frac{11}{20}x = \frac{39}{70}$$

$$x = \frac{39}{70} : \frac{11}{20}$$

$$x = \frac{39}{70} \cdot \frac{20}{11}$$

$$x = \frac{39 \cdot 20}{70 \cdot 11}$$

$$x = \frac{39 \cdot 2}{7 \cdot 11}$$

$$x = \frac{78}{77} = 1 \frac{1}{77}$$

Ответ: $$x = 1 \frac{1}{77}$$

4) $$2 \frac{2}{3}x - 1 \frac{1}{4} = 3 \frac{5}{6}$$

$$\frac{8}{3}x - \frac{5}{4} = \frac{23}{6}$$

$$\frac{8}{3}x = \frac{23}{6} + \frac{5}{4}$$

$$\frac{8}{3}x = \frac{23 \cdot 2 + 5 \cdot 3}{12}$$

$$\frac{8}{3}x = \frac{46 + 15}{12}$$

$$\frac{8}{3}x = \frac{61}{12}$$

$$x = \frac{61}{12} : \frac{8}{3}$$

$$x = \frac{61}{12} \cdot \frac{3}{8}$$

$$x = \frac{61 \cdot 3}{12 \cdot 8}$$

$$x = \frac{61 \cdot 1}{4 \cdot 8}$$

$$x = \frac{61}{32} = 1 \frac{29}{32}$$

Ответ: $$x = 1 \frac{29}{32}$$

5) $$5 \frac{1}{6} - 2 \frac{1}{8}x = 1 \frac{3}{4}$$

$$\frac{31}{6} - \frac{17}{8}x = \frac{7}{4}$$

$$\frac{17}{8}x = \frac{31}{6} - \frac{7}{4}$$

$$\frac{17}{8}x = \frac{31 \cdot 2 - 7 \cdot 3}{12}$$

$$\frac{17}{8}x = \frac{62 - 21}{12}$$

$$\frac{17}{8}x = \frac{41}{12}$$

$$x = \frac{41}{12} : \frac{17}{8}$$

$$x = \frac{41}{12} \cdot \frac{8}{17}$$

$$x = \frac{41 \cdot 8}{12 \cdot 17}$$

$$x = \frac{41 \cdot 2}{3 \cdot 17}$$

$$x = \frac{82}{51} = 1 \frac{31}{51}$$

Ответ: $$x = 1 \frac{31}{51}$$

6) $$\frac{3}{10}x + 1 \frac{2}{5} = 6 \frac{1}{2}$$

$$\frac{3}{10}x + \frac{7}{5} = \frac{13}{2}$$

$$\frac{3}{10}x = \frac{13}{2} - \frac{7}{5}$$

$$\frac{3}{10}x = \frac{13 \cdot 5 - 7 \cdot 2}{10}$$

$$\frac{3}{10}x = \frac{65 - 14}{10}$$

$$\frac{3}{10}x = \frac{51}{10}$$

$$x = \frac{51}{10} : \frac{3}{10}$$

$$x = \frac{51}{10} \cdot \frac{10}{3}$$

$$x = \frac{51}{3} = 17$$

Ответ: $$x = 17$$