Answer :
The number of innings Barron might have pitched before his latest game, is obtained as follows:
[tex]\begin{gathered} x+6\frac{2}{3}\ge82\frac{1}{3} \\ \Rightarrow x\text{ }\ge82\frac{1}{3}-6\frac{2}{3} \\ \Rightarrow x\text{ }\ge81\frac{4}{3}-6\frac{2}{3} \\ \Rightarrow x\text{ }\ge(81-6)(\frac{4}{3}-\frac{2}{3}) \\ \Rightarrow x\text{ }\ge(75)(\frac{2}{3}) \\ \Rightarrow x\text{ }\ge75\frac{2}{3} \end{gathered}[/tex]Thus, the number of innings Barron might have pitched before his latest game is:
[tex]\Rightarrow x\text{ }\ge75\frac{2}{3}\text{ innings}[/tex]