let's firstly convert the mixed fractions to improper fractions and proceed from there.
[tex]\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}~\hfill \stackrel{mixed}{7\frac{x}{3}}\implies \cfrac{7\cdot 3+x}{3}\implies \stackrel{improper}{\cfrac{21+x}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{26}{3}=\cfrac{21+x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{26}{3} \right)=3\left( \cfrac{21+x}{3} \right)}\implies 26=21+x\implies \boxed{5=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\frac{2}{3}=7\frac{5}{3}~\hfill[/tex]
