Giải:
\(\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|.\dfrac{2}{5}-1\dfrac{1}{3}=2\)
\(\Leftrightarrow\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|.\dfrac{2}{5}-\dfrac{4}{3}=2\)
\(\Leftrightarrow\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|.\dfrac{2}{5}=2+\dfrac{4}{3}\)
\(\Leftrightarrow\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|.\dfrac{2}{5}=\dfrac{10}{3}\)
\(\Leftrightarrow\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|=\dfrac{10}{3}:\dfrac{2}{5}\)
\(\Leftrightarrow\left|\dfrac{3}{4}-\dfrac{1}{2}x\right|=\dfrac{25}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{4}-\dfrac{1}{2}x=\dfrac{25}{3}\\\dfrac{3}{4}-\dfrac{1}{2}x=-\dfrac{25}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=-\dfrac{91}{12}\\\dfrac{1}{2}x=\dfrac{109}{12}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{91}{6}\\x=\dfrac{109}{6}\end{matrix}\right.\)
Vậy \(x=-\dfrac{91}{6}\) hoặc \(x=\dfrac{109}{6}\).
Chúc bạn học tốt!!!
\(| \dfrac{3}{4} - \dfrac{1}{2}x| . \dfrac{2}{5} - 1\dfrac{1}{3} = 2\)
\(|\dfrac{3}{4} - \dfrac{1}{2}x| . \dfrac{2}{5} = 2 + \dfrac{4}{3}\)
\(|\dfrac{3}{4} - \dfrac{1}{2}x| . \dfrac{2}{5} = \dfrac{10}{3}\)
\(|\dfrac{3}{4} - \dfrac{1}{2}x| = \dfrac{10}{3} : \dfrac{2}{5}\)
\(| \dfrac{3}{4} - \dfrac{1}{2}x| = \dfrac{25}{3}\)
\(\dfrac{3}{4} - \dfrac{1}{2}x = \dfrac{25}{3}\) hoặc \(\dfrac{3}{4} - \dfrac{1}{2}x = \dfrac{-25}{3}\)
\(\dfrac{1}{2}x = \dfrac{3}{4} - \dfrac{25}{3}\) hoặc \(\dfrac{1}{2}x = \dfrac{3}{4} + \dfrac{25}{3}\)
\(\dfrac{1}{2}x = \dfrac{-91}{12}\) hoặc \(\dfrac{1}{2}x = \dfrac{109}{12}\)
\(x = \dfrac{-91}{6}\) hoặc \(x = \dfrac{109}{6}\)
Vậy \(x = \dfrac{-91}{6}\) hoặc \(x = \dfrac{109}{6}\)
