4. Решите уравнение: a) $$x-\frac{8}{15}x=4\frac{1}{5}$$ б) $$\frac{2}{7}c+\frac{2}{3}c-\frac{11}{21}c=3\frac{1}{2}$$

а) $$x-\frac{8}{15}x=4\frac{1}{5}$$

1) $$x-\frac{8}{15}x = \frac{15}{15}x - \frac{8}{15}x = \frac{7}{15}x$$

Тогда, $$\frac{7}{15}x = 4\frac{1}{5}$$

$$x = 4\frac{1}{5} : \frac{7}{15} = \frac{21}{5} : \frac{7}{15} = \frac{21}{5} \cdot \frac{15}{7} = \frac{21 \cdot 15}{5 \cdot 7} = \frac{3 \cdot 7 \cdot 3 \cdot 5}{5 \cdot 7} = 9$$

б) $$\frac{2}{7}c+\frac{2}{3}c-\frac{11}{21}c=3\frac{1}{2}$$

1) Приведем дроби к общему знаменателю: $$\frac{2}{7}c+\frac{2}{3}c-\frac{11}{21}c = \frac{6}{21}c+\frac{14}{21}c-\frac{11}{21}c$$

2) $$\frac{6}{21}c+\frac{14}{21}c-\frac{11}{21}c = (\frac{6+14-11}{21})c = \frac{9}{21}c = \frac{3}{7}c$$

Тогда $$\frac{3}{7}c = 3\frac{1}{2}$$

$$c = 3\frac{1}{2} : \frac{3}{7} = \frac{7}{2} : \frac{3}{7} = \frac{7}{2} \cdot \frac{7}{3} = \frac{7 \cdot 7}{2 \cdot 3} = \frac{49}{6} = 8\frac{1}{6}$$

Ответ: a) $$x = 9$$; б) $$c = 8\frac{1}{6}$$