$$ \begin{aligned} 2x+\frac{5}{7} &= 0&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7\cdot2x+7\cdot\frac{5}{7} &= 7\cdot0&& \text{cancel out the denominators} \\[1 em]14x+5 &= 0&& \text{ move the constants to the right } \\[1 em]14x &= -5&& \text{ divide both sides by $ 14 $ } \\[1 em]x &= -\frac{5}{14}&& \\[1 em] \end{aligned} $$

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