c) \(\frac{1}{7}(\frac{2}{5}(\frac{5}{14}(x-2) + \frac{6}{7}) - \frac{5}{2}) = 0;\)

Решение:

Умножим обе части на 7:

\( \frac{2}{5}(\frac{5}{14}(x-2) + \frac{6}{7}) - \frac{5}{2} = 0 \)

Прибавим \(\frac{5}{2}\) к обеим частям:

\( \frac{2}{5}(\frac{5}{14}(x-2) + \frac{6}{7}) = \frac{5}{2} \)

Умножим обе части на \(\frac{5}{2}\):

\( \frac{5}{14}(x-2) + \frac{6}{7} = \frac{5}{2} \cdot \frac{5}{2} \)

\( \frac{5}{14}(x-2) + \frac{6}{7} = \frac{25}{4} \)

Вычтем \(\frac{6}{7}\) из обеих частей:

\( \frac{5}{14}(x-2) = \frac{25}{4} - \frac{6}{7} \)

\( \frac{5}{14}(x-2) = \frac{25 \cdot 7 - 6 \cdot 4}{28} \)

\( \frac{5}{14}(x-2) = \frac{175 - 24}{28} \)

\( \frac{5}{14}(x-2) = \frac{151}{28} \)

Умножим обе части на \(\frac{14}{5}\):

\( x-2 = \frac{151}{28} \cdot \frac{14}{5} \)

\( x-2 = \frac{151 \cdot 1}{2 \cdot 5} \)

\( x-2 = \frac{151}{10} \)

\( x = \frac{151}{10} + 2 \)

\( x = \frac{151 + 20}{10} \)

\( x = \frac{171}{10} \)

Ответ: \( x = \frac{171}{10} \).