$$ \begin{aligned} 5x-2(2x-7) &= 2(3x-1)+\frac{7}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot5x-2\cdot2(2x-7) &= 2\cdot2(3x-1)+2\cdot\frac{7}{2}&& \text{cancel out the denominators} \\[1 em]10x-(8x-28) &= 12x-4+7&& \text{simplify left and right hand side} \\[1 em]10x-8x+28 &= 12x+3&& \\[1 em]2x+28 &= 12x+3&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]2x-12x &= 3-28&& \text{simplify left and right hand side} \\[1 em]-10x &= -25&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{-25}{-10}&& \\[1 em]x &= \frac{5}{2}&& \\[1 em] \end{aligned} $$

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