$$ \begin{aligned} \frac{1}{2}x+6 &= x+10&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x+2\cdot6 &= 2x+2\cdot10&& \text{cancel out the denominators} \\[1 em]x+12 &= 2x+20&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]x-2x &= 20-12&& \text{simplify left and right hand side} \\[1 em]-x &= 8&& \text{switch signs on both sides} \\[1 em]x &= -8&& \\[1 em] \end{aligned} $$

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