4. Решите уравнение: a) y - 2 1/5 = 5 2/5; б) 13/21 (x - 3 13/21) + 2 10/21 = 7 2/21.

Решение:

a) $$y - 2 \frac{1}{5} = 5 \frac{2}{5}$$

$$y = 5 \frac{2}{5} + 2 \frac{1}{5}$$

$$y = 7 \frac{3}{5}$$

Ответ: $$7 \frac{3}{5}$$

б) $$\frac{13}{21} (x - 3 \frac{13}{21}) + 2 \frac{10}{21} = 7 \frac{2}{21}$$

$$\frac{13}{21} (x - 3 \frac{13}{21}) = 7 \frac{2}{21} - 2 \frac{10}{21}$$

$$\frac{13}{21} (x - 3 \frac{13}{21}) = 6 \frac{23}{21} - 2 \frac{10}{21}$$

$$\frac{13}{21} (x - 3 \frac{13}{21}) = 4 \frac{13}{21}$$

$$x - 3 \frac{13}{21} = 4 \frac{13}{21} : \frac{13}{21}$$

$$x - 3 \frac{13}{21} = \frac{97}{21} : \frac{13}{21}$$

$$x - 3 \frac{13}{21} = \frac{97}{21} \cdot \frac{21}{13}$$

$$x - 3 \frac{13}{21} = \frac{97}{13}$$

$$x = \frac{97}{13} + 3 \frac{13}{21}$$

$$x = 7 \frac{6}{13} + 3 \frac{13}{21}$$

$$x = 7 \frac{126}{273} + 3 \frac{169}{273}$$

$$x = 10 \frac{295}{273} = 11 \frac{22}{273}$$

Ответ: $$11 \frac{22}{273}$$