$$ \begin{aligned} \frac{2}{3}+\frac{7}{4}x-\frac{8}{14} &= 0&& \text{multiply ALL terms by } \color{blue}{ 84 }. \\[1 em]84\cdot\frac{2}{3}+84\frac{7}{4}x-84\cdot\frac{8}{14} &= 84\cdot0&& \text{cancel out the denominators} \\[1 em]56+147x-48 &= 0&& \text{simplify left side} \\[1 em]147x+8 &= 0&& \text{ move the constants to the right } \\[1 em]147x &= -8&& \text{ divide both sides by $ 147 $ } \\[1 em]x &= -\frac{8}{147}&& \\[1 em] \end{aligned} $$

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