2. Реши уравнения: a) -\( \frac{7}{13} \) (\( \frac{26}{27} \) + x) - (\( \frac{4}{9} \) - x) = 5\( \frac{1}{27} \); b) \( \frac{2x+5}{4} = \frac{x-3}{3} \).

Решение:

1. Уравнение а)

-\(\frac{7}{13}\)(\(\frac{26}{27}\) + x) - (\(\frac{4}{9}\) - x) = 5\(\frac{1}{27}\)

-\(\frac{7}{13}\) \(\cdot\) \(\frac{26}{27}\) - \(\frac{7}{13}\)x - \(\frac{4}{9}\) + x = \(\frac{136}{27}\)

-\(\frac{7 \cdot 2}{27}\) - \(\frac{7}{13}\)x - \(\frac{4}{9}\) + x = \(\frac{136}{27}\)

-\(\frac{14}{27}\) - \(\frac{7}{13}\)x - \(\frac{12}{27}\) + x = \(\frac{136}{27}\)

x - \(\frac{7}{13}\)x = \(\frac{136}{27}\) + \(\frac{14}{27}\) + \(\frac{12}{27}\)

\(\frac{13x-7x}{13}\) = \(\frac{136+14+12}{27}\)

\(\frac{6x}{13}\) = \(\frac{162}{27}\)

\(\frac{6x}{13}\) = 6

6x = 6 \(\cdot\) 13

x = 13

2. Уравнение б)

\(\frac{2x+5}{4} = \frac{x-3}{3}\)

3(2x+5) = 4(x-3)

6x + 15 = 4x - 12

6x - 4x = -12 - 15

2x = -27

x = -\(\frac{27}{2}\)

Ответ: а) x = 13; б) x = -13,5.