$$ \begin{aligned} \frac{1}{9}c+\frac{1}{2} &= \frac{5}{7}&& \text{multiply ALL terms by } \color{blue}{ 126 }. \\[1 em]126 \cdot \frac{1}{9}c+126\cdot\frac{1}{2} &= 126\cdot\frac{5}{7}&& \text{cancel out the denominators} \\[1 em]14c+63 &= 90&& \text{ move 63 to the right } \\[1 em]14c &= 90-63&& \\[1 em]14c &= 27&& \text{ divide both sides by $ 14 $ } \\[1 em]c &= \frac{27}{14}&& \\[1 em] \end{aligned} $$

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