$$ \begin{aligned} \frac{1}{3}(x+1) &= 2(x-4)&& \text{simplify left and right hand side} \\[1 em]\frac{x+1}{3} &= 2x-8&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{x+1}{3} &= 3\cdot2x-3\cdot8&& \text{cancel out the denominators} \\[1 em]x+1 &= 6x-24&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]x-6x &= -24-1&& \text{simplify left and right hand side} \\[1 em]-5x &= -25&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-25}{-5}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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