$$ \begin{aligned} x-8 &= 3x+\frac{20}{7}&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7x-7\cdot8 &= 7\cdot3x+7\cdot\frac{20}{7}&& \text{cancel out the denominators} \\[1 em]7x-56 &= 21x+20&& \text{move the $ \color{blue}{ 21x } $ to the left side and $ \color{blue}{ -56 }$ to the right} \\[1 em]7x-21x &= 20+56&& \text{simplify left and right hand side} \\[1 em]-14x &= 76&& \text{ divide both sides by $ -14 $ } \\[1 em]x &= -\frac{76}{14}&& \\[1 em]x &= -\frac{38}{7}&& \\[1 em] \end{aligned} $$

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