$$ \begin{aligned} x+7 &= \frac{1}{2}x+9&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2\cdot7 &= 2 \cdot \frac{1}{2}x+2\cdot9&& \text{cancel out the denominators} \\[1 em]2x+14 &= x+18&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 14 }$ to the right} \\[1 em]2x-x &= 18-14&& \text{simplify left and right hand side} \\[1 em]x &= 4&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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