Answer
$b= \frac{64}{3}$
Work Step by Step
Given \begin{equation}
\frac{2}{3}(b+5)=\frac{5}{6} b-\frac{2}{9}.
\end{equation} Rewrite each side as a fraction, then solve for $b$:
\begin{equation}
\begin{aligned} \frac{2}{3}(b+5)&=\frac{5}{6} b-\frac{2}{9}\\
\frac{2}{3} b+\frac{10}{3}&= \frac{5}{6} b-\frac{2}{9} \\
\frac{10}{3}+\frac{2}{9}&=\frac{5}{6} b-\frac{2}{3} b \\
\frac{10\cdot 3+ 2}{9}&= \frac{5b-2\cdot 2b}{6}\\
\frac{32}{9}&= \frac{b}{6}\\
\frac{32}{9}\cdot 6& = b\\
\frac{64}{3}& = b.
\end{aligned}
\end{equation} Check \begin{equation}
\begin{aligned}
\frac{2}{3}\cdot\left(\frac{64}{3}+5\right)& \stackrel{?}{=}\frac{5}{6}\cdot \frac{64}{3}-\frac{2}{9}\\
\frac{158}{9}& =\frac{158}{9}\quad \textbf{True}
\end{aligned}
\end{equation} The solution is $b= \frac{64}{3}$.
