\(1)\) \(2x-\dfrac{1}{4}=\dfrac{6}{18}.\dfrac{9}{2}\)
\(2x-\dfrac{1}{4}=\dfrac{3}{2}\)
\(2x=\dfrac{3}{2}+\dfrac{1}{4}\)
\(2x=\dfrac{6}{4}+\dfrac{1}{4}\)
\(2x=\dfrac{7}{4}\)
\(x=\dfrac{7}{8}\)
\(2)\) \(x-\dfrac{4}{5}=\dfrac{6}{20}.\dfrac{-7}{3}\)
\(x-\dfrac{4}{5}=\dfrac{-7}{10}\)
\(x=\dfrac{-7}{10}+\dfrac{4}{5}\)
\(x=\dfrac{-7}{10}+\dfrac{8}{10}\)
\(x=\dfrac{1}{10}\)
\(3)\) \(x+\dfrac{5}{6}=\dfrac{16}{42}.\dfrac{-8}{56}\)
\(x+\dfrac{5}{6}=\dfrac{8}{21}.\dfrac{-1}{7}\)
\(x+\dfrac{5}{6}=\dfrac{-8}{147}\)
\(x=\dfrac{-8}{147}-\dfrac{5}{6}\)
\(x=\dfrac{-87}{98}\)
\(4)\) \(\left(\dfrac{1}{3}-2x\right).\dfrac{2}{5}=\dfrac{-8}{25}\)
\(\dfrac{1}{3}-2x=\dfrac{-8}{25}:\dfrac{2}{5}\)
\(\dfrac{1}{3}-2x=\dfrac{-8}{25}\times\dfrac{5}{2}\)
\(\dfrac{1}{3}-2x=\dfrac{-4}{5}\)
\(2x=\dfrac{1}{3}-\dfrac{-4}{5}\)
\(2x=\dfrac{5}{15}-\dfrac{-12}{15}\)
\(2x=\dfrac{17}{15}\)
\(x=\dfrac{17}{30}\)