$$ \begin{aligned} \frac{x}{2}-1 &= \frac{2}{3}x+5&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x}{2}-6\cdot1 &= 6 \cdot \frac{2}{3}x+6\cdot5&& \text{cancel out the denominators} \\[1 em]3x-6 &= 4x+30&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]3x-4x &= 30+6&& \text{simplify left and right hand side} \\[1 em]-x &= 36&& \text{switch signs on both sides} \\[1 em]x &= -36&& \\[1 em] \end{aligned} $$

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