[tex]3 \frac{1}{4}+ \frac{x}{6}= \frac{1}{2} + \frac{x}{9} \\
\frac{13}{4} + \frac{x}{6}= \frac{1}{2} + \frac{x}{9} \\
\frac{x}{6}- \frac{x}{9}=\frac{1}{2} - \frac{13}{4} \\
\frac{9x-6x}{54}= \frac{2-13}{4} \\
\frac{3x}{54} =- \frac{11}{4}\\
\frac{1}{18}x= - \frac{11}{4}\\
x=- \frac{11}{4}: \frac{1}{18}\\
x=-\frac{11}{4}*\frac{18}{1}\\
x=- \frac{99}{2} [/tex]