\[\boxed{\mathbf{2.469}}\]
\[\textbf{а)}\ 1\frac{5}{7}\ :x = \frac{6}{7}\ :2\]
\[\frac{6}{7}x = \frac{12}{7} \cdot 2\]
\[\frac{6}{7}x = \frac{24}{7}\]
\[x = \frac{24}{7}\ :\frac{6}{7} = \frac{24}{7} \cdot \frac{7}{6}\]
\[x = 4\]
\[Ответ:x = 4.\]
\[\textbf{б)}\ a\ :1\frac{3}{4} = 1\frac{3}{4} \cdot \frac{1}{4}\]
\[a\ :\frac{7}{4} = \frac{7}{4} \cdot \frac{1}{4}\]
\[a = \frac{7}{16} \cdot \frac{7}{4}\]
\[a = \frac{49}{64}\]
\[Ответ:a = \frac{49}{64}.\]
\[\textbf{в)}\ 1\frac{2}{3} \cdot \left( \frac{1}{3}n + \frac{3}{7} \right) = 2\frac{1}{4}\]
\[\frac{1}{3}n + \frac{3}{7} = \frac{9}{4}\ :\frac{5}{3}\]
\[\frac{1}{3}n + \frac{3}{7} = \frac{9}{4} \cdot \frac{3}{5}\]
\[\frac{1}{3}n = \frac{27}{20} - \frac{3}{7}\]
\[\frac{1}{3}n = \frac{189}{140} - \frac{60}{140} = \frac{129}{140}\]
\[n = \frac{129}{140}\ :\frac{1}{3} = \frac{129}{140} \cdot 3\]
\[n = \frac{387}{140} = 2\frac{107}{140}\]
\[Ответ:n = 2\frac{107}{140}.\]
\[\textbf{г)}\ \left( \frac{5}{4}z - \frac{3}{5} \right) \cdot \frac{7}{8} = \frac{7}{8}\]
\[\frac{5}{4}z - \frac{3}{5} = 1\]
\[\frac{5}{4}z = 1 + \frac{3}{5}\]
\[\frac{5}{4}z = 1\frac{3}{5}\]
\[z = \frac{8}{5}\ :\frac{5}{4} = \frac{8}{5} \cdot \frac{4}{5}\]
\[z = \frac{32}{25} = 1\frac{7}{25}\]
\[Ответ:z = 1\frac{7}{25}\text{.\ }\]