\(TH1:x\ge0\)
\(\Rightarrow x\left(1-\dfrac{5}{6}\right)=\dfrac{4}{9}.\dfrac{15}{8}\)
\(\Rightarrow x=\dfrac{\dfrac{4}{9}.\dfrac{15}{8}}{1-\dfrac{5}{6}}=5\left(TM\right)\)
\(TH2:x< 0\)
\(\Rightarrow x\left(-1-\dfrac{5}{6}\right)=\dfrac{4}{9}.\dfrac{15}{8}\)
\(\Rightarrow x=\dfrac{\dfrac{4}{9}.\dfrac{15}{8}}{-1-\dfrac{5}{6}}=-\dfrac{5}{11}\left(TM\right)\)
Vậy ...
Giải:
\(\left|x\right|-\dfrac{5}{6}.x=\dfrac{4}{9}.\dfrac{15}{8}\)
\(TH1:x\ge0\)
\(\left|x\right|-\dfrac{5}{6}.x=\dfrac{4}{9}.\dfrac{15}{8}\)
\(x-\dfrac{5}{6}.x=\dfrac{5}{6}\)
\(x.\left(1-\dfrac{5}{6}\right)=\dfrac{5}{6}\)
\(x.\dfrac{1}{6}=\dfrac{5}{6}\)
\(x=\dfrac{5}{6}:\dfrac{1}{6}\)
\(x=5\)
\(TH2:x\le0\)
\(\left|x\right|-\dfrac{5}{6}.x=\dfrac{4}{9}.\dfrac{15}{8}\)
\(-x-\dfrac{5}{6}.x=\dfrac{5}{6}\)
\(x.\left(-1-\dfrac{5}{6}\right)=\dfrac{5}{6}\)
\(x.\dfrac{-11}{6}=\dfrac{5}{6}\)
\(x=\dfrac{5}{6}:\dfrac{-11}{6}\)
\(x=\dfrac{-5}{11}\)
Vậy \(x\in\left\{\dfrac{-5}{11};5\right\}\)
