$$ \begin{aligned} \frac{1}{2}x+2 &= 1&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x+2\cdot2 &= 2\cdot1&& \text{cancel out the denominators} \\[1 em]x+4 &= 2&& \text{ move 4 to the right } \\[1 em]x &= 2-4&& \\[1 em]x &= -2&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$
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