$$ \begin{aligned} 5x-\frac{1}{2} &= 4+\frac{3}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot5x-2\cdot\frac{1}{2} &= 2\cdot4+2 \cdot \frac{3}{2}x&& \text{cancel out the denominators} \\[1 em]10x-1 &= 8+3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]10x-3x &= 8+1&& \text{simplify left and right hand side} \\[1 em]7x &= 9&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{9}{7}&& \\[1 em] \end{aligned} $$

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