$\begin{array}{l}
1)\dfrac{{ - 7}}{{18}} + \dfrac{{ - 5}}{6} + \dfrac{{ - 11}}{{12}} = \dfrac{{ - 14}}{{36}} + \dfrac{{ - 30}}{{36}} - \dfrac{{ - 33}}{{36}} = \dfrac{{ - 77}}{{36}}\\
2)\dfrac{{ - 5}}{9} + \dfrac{5}{9}:\left( {1\dfrac{2}{3} - 2\dfrac{1}{{12}}} \right) = - \dfrac{5}{9} + \dfrac{5}{9}:\left( {\dfrac{5}{3} - \dfrac{{25}}{{12}}} \right) = \dfrac{{ - 5}}{9} + \dfrac{5}{9}:\left( {\dfrac{{5.4 - 25}}{{12}}} \right) = \dfrac{{ - 5}}{9} + \dfrac{5}{9}:\dfrac{{ - 5}}{{12}} = \dfrac{{ - 17}}{9}\\
3)\dfrac{{ - 7}}{{25}}.\dfrac{{11}}{{13}} + \dfrac{{ - 7}}{{25}}.\dfrac{2}{3}. - \dfrac{{18}}{{25}} = \dfrac{{ - 7}}{{25}}\left( {\dfrac{{11}}{{13}} - \dfrac{2}{3}} \right) - \dfrac{{18}}{{25}} = \dfrac{{ - 751}}{{975}}\\
4)x + \dfrac{{ - 7}}{{15}} = - 1\dfrac{1}{{20}} \Rightarrow x = \dfrac{{ - 21}}{{20}} - \dfrac{7}{{15}} = \dfrac{{ - 63 - 28}}{{60}} = \dfrac{{ - 91}}{{60}}\\
5)\dfrac{{ - 2}}{3} + \dfrac{4}{5}x = \dfrac{1}{5} \Rightarrow \dfrac{4}{5}x = \dfrac{1}{5} + \dfrac{2}{3} = \dfrac{{13}}{{15}} \Rightarrow x = \dfrac{{13}}{{15}}:\dfrac{4}{5} = \dfrac{{13}}{{12}}\\
6)2\left| x \right| - \dfrac{1}{2} = \dfrac{1}{4} \Rightarrow 2\left| x \right| = \dfrac{1}{4} + \dfrac{1}{2} = \dfrac{3}{4} \Rightarrow \left[ \begin{array}{l}
x = \dfrac{3}{8}\\
x = \dfrac{{ - 3}}{8}
\end{array} \right.
\end{array}$
