$$ \begin{aligned} 3 \cdot \frac{x}{2}-\frac{7}{2} &= 5x+14&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3 \cdot \frac{x}{2}-2\cdot\frac{7}{2} &= 2\cdot5x+2\cdot14&& \text{cancel out the denominators} \\[1 em]3x-7 &= 10x+28&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]3x-10x &= 28+7&& \text{simplify left and right hand side} \\[1 em]-7x &= 35&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= -\frac{35}{7}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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