\(5\frac{1}{2}-5\frac{1}{3}.\left(\frac{3}{2}.x-\frac{1}{3}\right)=1\frac{1}{2}\)
\(\frac{16}{3}\left(\frac{3}{2}.x-\frac{1}{2}\right)=5\frac{1}{2}-1\frac{1}{2}=4\)
\(\frac{3}{2}x-\frac{1}{2}=4:\frac{16}{3}=\frac{4}{3}\)
\(\frac{3}{2}x=\frac{4}{3}+\frac{1}{2}=\frac{11}{6}\)
\(x=\frac{11}{6}:\frac{3}{2}\)
\(x=\frac{11}{9}\)