$$ \begin{aligned} \frac{3}{4}(2x-1) &= \frac{1}{2}(4x+2)&& \text{simplify left and right hand side} \\[1 em]\frac{6x-3}{4} &= \frac{4x+2}{2}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{6x-3}{4} &= 4 \cdot \frac{4x+2}{2}&& \text{cancel out the denominators} \\[1 em]6x-3 &= 8x+4&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]6x-8x &= 4+3&& \text{simplify left and right hand side} \\[1 em]-2x &= 7&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{7}{2}&& \\[1 em] \end{aligned} $$

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