$$\frac{1}{2}x+2 = 2x-1$$

$$ \begin{aligned} \frac{1}{2}x+2 &= 2x-1&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}x+2\cdot2 &= 2\cdot2x-2\cdot1&& \text{cancel out the denominators} \\[1 em]x+4 &= 4x-2&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]x-4x &= -2-4&& \text{simplify left and right hand side} \\[1 em]-3x &= -6&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= \frac{-6}{-3}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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