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

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

\(x = \frac{- 26}{15}\).

b) \(\frac{- 5}{6} + \frac{1}{3} . x = \left(\right. \frac{- 1}{2} \left.\right)^{2}\);

\(\frac{- 5}{6} + \frac{1}{3} . x = \frac{1}{4}\)

\(\frac{1}{3} . x = \frac{1}{4} + \frac{5}{6}\)

\(\frac{1}{3} . x = \frac{13}{12}\)

\(x = \frac{13}{12} : \frac{1}{3}\)

\(x = \frac{13}{4}\).

c) \(\frac{7}{12} - \left(\right. x + \frac{7}{6} \left.\right) . \frac{6}{5} = \left(\right. \frac{- 1}{2} \left.\right)^{3}\).

\(\frac{7}{12} - \left(\right. x + \frac{7}{6} \left.\right) . \frac{6}{5} = \frac{- 1}{8}\)

\(\left(\right. x + \frac{7}{6} \left.\right) . \frac{6}{5} = \frac{7}{12} - \left(\right. \frac{- 1}{8} \left.\right)\)

\(\left(\right.x+\frac{7}{6}\left.\right).\frac{6}{5}=\frac{17}{24}\)

\(x+\frac{7}{6}=\frac{85}{144}\)

\(x=\frac{85}{144}-\frac{7}{6}\)

\(x=\frac{- 83}{144}\).

a) \(\frac{4}{9} + \frac{1}{4} = \frac{16}{36} + \frac{9}{36} = \frac{25}{36}\).

\(b \left.\right)\) \(\frac{1}{3} . \left(\right. \frac{- 4}{5} \left.\right) + \frac{1}{3} . \frac{- 1}{5}\)

\(=\frac{1}{3}.\left(\right.\frac{- 4}{5}+\frac{- 1}{5};\left.\right)\)

\(=\frac{1}{3}.\left(\right.-1\left.\right)\)

\(= - \frac{1}{3}\).

\(c \left.\right)\) \(\frac{1}{5} - \left[\right. \frac{1}{4} - \left(\right. 1 - \frac{1}{2} \left.\right)^{2} \left]\right.\).

\(= \frac{1}{5} - \left[\right. \frac{1}{4} - \left(\right. \frac{1}{2} \left.\right)^{2} \left]\right.\)

\(= \frac{1}{5} - \left[\right. \frac{1}{4} - \frac{1}{4} \left]\right.\)

\(= \frac{1}{5} - 0 = \frac{1}{5}\)

a) \(​ \frac{11}{24} - \frac{5}{41} + \frac{13}{24} + 0 , 5 - \frac{36}{41} = \left(\right. \frac{11}{24} + \frac{13}{24} \left.\right) - \left(\right. \frac{5}{41} + \frac{36}{41} \left.\right) + 0 , 5 = 1 - 1 + 0 , 5 = 0 , 5\).

b) \(\frac{1}{2} \cdot \frac{3}{4} + \frac{1}{2} \cdot \frac{1}{4} + \frac{1}{2} = \frac{1}{2} \cdot \left(\right. \frac{3}{4} + \frac{1}{4} + 1 \left.\right) = \frac{1}{2} \cdot 2 = 1\).

c) \(\left(\right. \frac{- 3}{4} \left.\right)^{2} : \left(\right. \frac{- 1}{4} \left.\right)^{2} + 9 \cdot \left(\right. \frac{- 1}{9} \left.\right) + \left(\right. \frac{- 3}{2} \left.\right) = \frac{9}{16} : \frac{1}{16} - 1 - \frac{3}{2} = 9 - 1 - \frac{3}{2} = \frac{13}{2} .\)

d) \(\sqrt{0 , 25} \cdot \left(\right. - 3 \left.\right)^{3} - \sqrt{\frac{1}{81}} : \left(\right. \frac{- 1}{3} \left.\right)^{3} = 0 , 5 \cdot \left(\right. - 27 \left.\right) - \frac{1}{9} : \frac{- 1}{27} = \frac{- 27}{2} + 3 = \frac{- 21}{2}\).