$$ \begin{aligned} \frac{1}{6}x+37 &= 61-\frac{1}{3}x&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{1}{6}x+6\cdot37 &= 6\cdot61-6 \cdot \frac{1}{3}x&& \text{cancel out the denominators} \\[1 em]x+222 &= 366-2x&& \text{move the $ \color{blue}{ -2x } $ to the left side and $ \color{blue}{ 222 }$ to the right} \\[1 em]x+2x &= 366-222&& \text{simplify left and right hand side} \\[1 em]3x &= 144&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{144}{3}&& \\[1 em]x &= 48&& \\[1 em] \end{aligned} $$

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