$$ \begin{aligned} x+\frac{2}{7} &= -14&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7x+7\cdot\frac{2}{7} &= 7\cdot(-14)&& \text{cancel out the denominators} \\[1 em]7x+2 &= -98&& \text{ move 2 to the right } \\[1 em]7x &= -98-2&& \\[1 em]7x &= -100&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{100}{7}&& \\[1 em] \end{aligned} $$

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