a) \(\dfrac{3}{7}x-2\dfrac{1}{3}=0,5\)

\(\Leftrightarrow\dfrac{3}{7}x-\dfrac{7}{3}=\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{3}{7}x=\dfrac{1}{2}+\dfrac{7}{3}\)

\(\Leftrightarrow\dfrac{3}{7}x=\dfrac{17}{6}\)

\(\Leftrightarrow x=\dfrac{17}{6}:\dfrac{3}{7}\)

\(\Leftrightarrow x=\dfrac{119}{18}\)

b) \(\dfrac{4}{7}-\dfrac{2}{3}:x=1\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{4}{7}-\dfrac{2}{3}:x=\dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{2}{3}:x=\dfrac{4}{7}-\dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{2}{3}:x=\dfrac{-19}{28}\)

\(\Leftrightarrow x=\dfrac{2}{3}:\dfrac{-19}{28}\)

\(\Leftrightarrow x=\dfrac{56}{-57}\)

c) \(\left(\dfrac{2}{3}x+2\dfrac{1}{4}\right):3\dfrac{1}{5}=0,75\)

\(\Leftrightarrow\left(\dfrac{2}{3}x+\dfrac{9}{4}\right):\dfrac{16}{6}=\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{2}{3}x+\dfrac{9}{4}=\dfrac{3}{4}.\dfrac{16}{6}\)

\(\Leftrightarrow\dfrac{2}{3}x+\dfrac{9}{4}=2\)

\(\Leftrightarrow\dfrac{2}{3}x=2-\dfrac{9}{4}\)

\(\Leftrightarrow\dfrac{2}{3}x=\dfrac{-1}{4}\)

\(\Leftrightarrow x=\dfrac{-1}{4}:\dfrac{2}{3}\)

\(\Leftrightarrow x=\dfrac{-3}{8}\)

d) \(\left|\dfrac{4}{5}-\dfrac{2}{3}x\right|:\dfrac{1}{4}-\dfrac{2}{3}=1\)

\(\Leftrightarrow\left|\dfrac{4}{5}-\dfrac{2}{3}x\right|:\dfrac{1}{4}=1+\dfrac{2}{3}\)

\(\Leftrightarrow\left|\dfrac{4}{5}-\dfrac{2}{3}x\right|:\dfrac{1}{4}=\dfrac{5}{3}\)

\(\Leftrightarrow\left|\dfrac{4}{5}-\dfrac{2}{3}x\right|=\dfrac{5}{3}.\dfrac{1}{4}\)

\(\Leftrightarrow\left|\dfrac{4}{5}-\dfrac{2}{3}x\right|=\dfrac{5}{12}\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{4}{5}-\dfrac{2}{3}x=\dfrac{5}{12}\\\dfrac{4}{5}-\dfrac{2}{3}x=-\dfrac{5}{12}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=\dfrac{4}{5}-\dfrac{5}{12}\\\dfrac{2}{3}x=\dfrac{4}{5}-\left(-\dfrac{5}{12}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=\dfrac{23}{60}\\\dfrac{2}{3}x=\dfrac{73}{60}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{23}{60}:\dfrac{2}{3}\\x=\dfrac{73}{60}:\dfrac{2}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{23}{20}\\x=\dfrac{73}{20}\end{matrix}\right.\)