$$ \begin{aligned} \frac{1}{3}x+1 &= x-5&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{1}{3}x+3\cdot1 &= 3x-3\cdot5&& \text{cancel out the denominators} \\[1 em]x+3 &= 3x-15&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]x-3x &= -15-3&& \text{simplify left and right hand side} \\[1 em]-2x &= -18&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-18}{-2}&& \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$

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