a) \(x+\dfrac{2}{5}=\dfrac{-4}{3}\)

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

\(x=\dfrac{-26}{15}\)

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

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

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

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

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

\(x=\dfrac{13}{4}\)

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

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

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

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

                           \(x+\dfrac{7}{6}=\dfrac{17}{24}:\dfrac{6}{5}\)

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

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

                                   \(x=\dfrac{-83}{144}\)