$$ \begin{aligned} x-\frac{13}{5} &= \frac{6}{7}&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35x-35\cdot\frac{13}{5} &= 35\cdot\frac{6}{7}&& \text{cancel out the denominators} \\[1 em]35x-91 &= 30&& \text{ move -91 to the right } \\[1 em]35x &= 30+91&& \\[1 em]35x &= 121&& \text{ divide both sides by $ 35 $ } \\[1 em]x &= \frac{121}{35}&& \\[1 em] \end{aligned} $$

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