$$5x+\frac{7}{2} = \frac{3}{2}x-14$$

$$ \begin{aligned} 5x+\frac{7}{2} &= \frac{3}{2}x-14&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot5x+2\cdot\frac{7}{2} &= 2 \cdot \frac{3}{2}x-2\cdot14&& \text{cancel out the denominators} \\[1 em]10x+7 &= 3x-28&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]10x-3x &= -28-7&& \text{simplify left and right hand side} \\[1 em]7x &= -35&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{35}{7}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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