$$ \begin{aligned} 5 \cdot \frac{x}{4}+\frac{1}{2} &= x-\frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot5 \cdot \frac{x}{4}+4\cdot\frac{1}{2} &= 4x-4\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]5x+2 &= 4x-2&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]5x-4x &= -2-2&& \text{simplify left and right hand side} \\[1 em]x &= -4&& \\[1 em]x &= -4&& \\[1 em] \end{aligned} $$

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