\(\Rightarrow\left|3x+1\right|=4+\dfrac{1}{2}=\dfrac{9}{2}\\ \Rightarrow\left[{}\begin{matrix}3x+1=\dfrac{9}{2}\\3x+1=-\dfrac{9}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=\dfrac{7}{2}\\3x=-\dfrac{11}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{6}\\x=-\dfrac{11}{6}\end{matrix}\right.\)
\(\Leftrightarrow\left|3x+1\right|=\dfrac{9}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=\dfrac{9}{2}\\3x+1=-\dfrac{9}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{6}\\x=-\dfrac{11}{6}\end{matrix}\right.\)
