Answer :
[tex]\frac{1}{3}x+\frac{1}{3}(2x-15)=3\frac{1}{2}\\\\
\frac{1}{3}x+\frac{1}{3}(2x-15)=\frac{7}{2}\ \ \ |Multiply\ by\ 6\\\\
2x+2(2x-15)=21\\\\
2x+4x-30=21\\\\
6x-30=21\ \ |Add\ 30\\\\
6x=51\ \ \ |Divide\ by\ 6\\\\
\boxed{x=\frac{51}{6}=8\frac{1}{2}}[/tex]