$$ \begin{aligned} \frac{1}{5}x+\frac{6}{5} &= \frac{8}{7}+\frac{1}{7}x&& \text{multiply ALL terms by } \color{blue}{ 35 }. \\[1 em]35 \cdot \frac{1}{5}x+35\cdot\frac{6}{5} &= 35\cdot\frac{8}{7}+35\frac{1}{7}x&& \text{cancel out the denominators} \\[1 em]7x+42 &= 40+5x&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 42 }$ to the right} \\[1 em]7x-5x &= 40-42&& \text{simplify left and right hand side} \\[1 em]2x &= -2&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{2}{2}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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