Write the mixed fraction on the right side as a proper fraction.
[tex]\begin{gathered} 3\frac{3}{8}=\frac{3\cdot8+3}{8} \\ =\frac{27}{8} \end{gathered}[/tex]The given equation becomes
[tex]\begin{gathered} \frac{3}{8}x=\frac{27}{8} \\ 3x=27 \\ x=\frac{27}{3}=9 \end{gathered}[/tex]The value of x is 9.