$$ \begin{aligned} \frac{7}{9}(m+3) &= 7&& \text{simplify left side} \\[1 em]\frac{7m+21}{9} &= 7&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{7m+21}{9} &= 9\cdot7&& \text{cancel out the denominators} \\[1 em]7m+21 &= 63&& \text{ move 21 to the right } \\[1 em]7m &= 63-21&& \\[1 em]7m &= 42&& \text{ divide both sides by $ 7 $ } \\[1 em]m &= \frac{42}{7}&& \\[1 em]m &= 6&& \\[1 em] \end{aligned} $$

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