\(\frac{1}{2}\left|\frac{3}{5}x-\frac{1}{3}\right|+\frac{1}{4}=\frac{5}{2}\)
\(\Leftrightarrow\frac{1}{2}\left|3x-\frac{1}{3}\right|=\frac{5}{2}-\frac{2}{4}\)
\(\Leftrightarrow\left|\frac{3}{5}x-\frac{1}{3}\right|=\frac{9}{2}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{3}{5}x-\frac{1}{3}=\frac{9}{2}\\\frac{3}{5}x-\frac{1}{3}=\frac{-9}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{3}{5}x=\frac{9}{2}+\frac{1}{3}\\\frac{3}{5}x=\frac{-9}{2}+\frac{1}{3}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{29}{6}:\frac{3}{5}\\x=\frac{-25}{6}:\frac{3}{5}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{145}{18}\\x=\frac{-125}{18}\end{cases}}\)