Ta có : \(\left|2x-1\right|-\frac{1}{2}=\frac{1}{3}\)
=> \(\left|2x-1\right|=\frac{5}{6}\)
TH1 : \(2x-1\ge0\left(x\ge\frac{1}{2}\right)\)
=> \(\left|2x-1\right|=2x-1=\frac{5}{6}\)
=> \(x=\frac{\frac{5}{6}+1}{2}=\frac{11}{12}\)( TM )
TH2 : \(2x-1< 0\left(x< \frac{1}{2}\right)\)
=> \(\left|2x-1\right|=1-2x=\frac{5}{6}\)
=> \(x=\frac{\frac{5}{6}-1}{-2}=\frac{1}{12}\) ( TM )
Vậy phương trình trên có tập nghiệm là \(S=\left\{\frac{1}{12};\frac{11}{12}\right\}\)
\(|2x-1|-\frac{1}{2}=\frac{1}{3}\)
\(|2x-1|=\frac{1}{3}+\frac{1}{2}\)
\(|2x-1|=\frac{2+3}{6}\)
\(|2x-1|=\frac{5}{6}\)
\(\Rightarrow2x-1=\frac{5}{6}\) hoặc \(2x-1=-\frac{5}{6}\)
\(TH1:2x-1=\frac{5}{6}\)
\(2x=\frac{5}{6}+1\)
\(2x=\frac{5+6}{6}\)
\(2x=\frac{11}{6}\)
\(x=\frac{11}{6}:2\)
\(x=\frac{11}{6}.\frac{1}{2}\)
\(x=\frac{11}{12}\)
\(TH2:2x-1=-\frac{5}{6}\)
\(2x=-\frac{5}{6}+1\)
\(2x=\frac{-5+6}{6}\)
\(2x=\frac{1}{6}\)
\(x=\frac{1}{6}:2\)
\(x=\frac{1}{6}.\frac{1}{2}\)
\(x=\frac{1}{12}\)
Vậy \(x\in\left\{\frac{11}{12};\frac{1}{12}\right\}\)
