$$ \begin{aligned} x+5 &= 14-\frac{1}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2\cdot5 &= 2\cdot14-2 \cdot \frac{1}{2}x&& \text{cancel out the denominators} \\[1 em]2x+10 &= 28-x&& \text{move the $ \color{blue}{ -x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]2x+x &= 28-10&& \text{simplify left and right hand side} \\[1 em]3x &= 18&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{18}{3}&& \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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