4. Решить уравнение: 1) $$8\frac{2}{39} - x = 4\frac{5}{26}$$; 2) $$4\frac{2}{7} + (x - 2\frac{1}{5}) = 5\frac{2}{3}$$

Решим уравнения пошагово. 1) $$8\frac{2}{39} - x = 4\frac{5}{26}$$ $$\frac{8\cdot39 + 2}{39} - x = \frac{4\cdot26 + 5}{26}$$ $$\frac{312+2}{39} - x = \frac{104+5}{26}$$ $$\frac{314}{39} - x = \frac{109}{26}$$ $$x = \frac{314}{39} - \frac{109}{26}$$ $$x = \frac{314\cdot26 - 109\cdot39}{39\cdot26}$$ $$x = \frac{8164 - 4251}{1014}$$ $$x = \frac{3913}{1014}$$ $$x = 3\frac{871}{1014}$$ $$x = 3\frac{67}{78}$$ Ответ: $$x = 3\frac{67}{78}$$ 2) $$4\frac{2}{7} + (x - 2\frac{1}{5}) = 5\frac{2}{3}$$ $$\frac{4\cdot7 + 2}{7} + (x - \frac{2\cdot5 + 1}{5}) = \frac{5\cdot3 + 2}{3}$$ $$\frac{28 + 2}{7} + (x - \frac{10+1}{5}) = \frac{15+2}{3}$$ $$\frac{30}{7} + x - \frac{11}{5} = \frac{17}{3}$$ $$x = \frac{17}{3} - \frac{30}{7} + \frac{11}{5}$$ $$x = \frac{17\cdot35 - 30\cdot15 + 11\cdot21}{105}$$ $$x = \frac{595 - 450 + 231}{105}$$ $$x = \frac{376}{105}$$ $$x = 3\frac{61}{105}$$ Ответ: $$x = 3\frac{61}{105}$$