$$ \begin{aligned} \frac{2}{3} &= \frac{1}{3}+\frac{1}{7}b&& \text{multiply ALL terms by } \color{blue}{ 21 }. \\[1 em]21\cdot\frac{2}{3} &= 21\cdot\frac{1}{3}+21\frac{1}{7}b&& \text{cancel out the denominators} \\[1 em]14 &= 7+3b&& \text{ swap the left and right side of the equation } \\[1 em]7+3b &= 14&& \text{ move 7 to the right } \\[1 em]3b &= 14-7&& \\[1 em]3b &= 7&& \text{ divide both sides by $ 3 $ } \\[1 em]b &= \frac{7}{3}&& \\[1 em] \end{aligned} $$

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