$$ \begin{aligned} \frac{5}{7}+7\frac{x}{5} &= \frac{88}{35}&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35\cdot\frac{5}{7}+35\cdot7\frac{x}{5} &= 35\cdot\frac{88}{35}&& \text{cancel out the denominators} \\[1 em]25+49x &= 88&& \text{ move 25 to the right } \\[1 em]49x &= 88-25&& \\[1 em]49x &= 63&& \text{ divide both sides by $ 49 $ } \\[1 em]x &= \frac{63}{49}&& \\[1 em]x &= \frac{9}{7}&& \\[1 em] \end{aligned} $$

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