$$ \begin{aligned} 3x-7 \cdot \frac{x^1}{2}+4 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3x-2\cdot7 \cdot \frac{x^1}{2}+2\cdot4 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]6x-7x+8 &= 0&& \text{simplify left side} \\[1 em]-x+8 &= 0&& \text{ move the constants to the right } \\[1 em]-x &= -8&& \text{switch signs on both sides} \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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