4. Решите уравнение: 1) x + \frac{4}{21}x = 8\frac{1}{3}; 2) \frac{7}{12}x + \frac{1}{6} = 16\frac{1}{2}.

4. Решите уравнение:

1) $$x + \frac{4}{21}x = 8\frac{1}{3}$$ $$x(1 + \frac{4}{21}) = \frac{8 \cdot 3 + 1}{3}$$ $$x(\frac{21}{21} + \frac{4}{21}) = \frac{24 + 1}{3}$$ $$x \cdot \frac{25}{21} = \frac{25}{3}$$ $$x = \frac{25}{3}:\frac{25}{21}$$ $$x = \frac{25}{3} \cdot \frac{21}{25}$$ $$x = \frac{25 \cdot 21}{3 \cdot 25}$$ $$x = \frac{7}{1} = 7$$

Ответ: 7

2) $$\frac{7}{12}x + \frac{1}{6} = 16\frac{1}{2}$$ $$\frac{7}{12}x = \frac{16 \cdot 2 + 1}{2} - \frac{1}{6}$$ $$\frac{7}{12}x = \frac{32 + 1}{2} - \frac{1}{6}$$ $$\frac{7}{12}x = \frac{33}{2} - \frac{1}{6}$$ $$\frac{7}{12}x = \frac{33 \cdot 3}{2 \cdot 3} - \frac{1}{6}$$ $$\frac{7}{12}x = \frac{99}{6} - \frac{1}{6}$$ $$\frac{7}{12}x = \frac{98}{6}$$ $$x = \frac{98}{6}:\frac{7}{12}$$ $$x = \frac{98}{6} \cdot \frac{12}{7}$$ $$x = \frac{98 \cdot 12}{6 \cdot 7}$$ $$x = \frac{14 \cdot 2}{1 \cdot 1} = 28$$

Ответ: 28