\(2\left|3x-1\right|+1=5\)
\(\Leftrightarrow2\left|3x-1\right|=5-1=4\)
\(\Leftrightarrow\left|3x-1\right|=\frac{4}{2}=2\)
\(\Leftrightarrow\hept{\begin{cases}3x-1=2\\3x-1=-2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}3x=3\\3x=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=1\\x=\frac{1}{3}\end{cases}}\)
Vậy \(x\in\left\{1;\frac{1}{3}\right\}\)