$$ \begin{aligned} \frac{2}{7}x+\frac{1}{7} &= -\frac{9}{7}&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{2}{7}x+7\cdot\frac{1}{7} &= -7\cdot\frac{9}{7}&& \text{cancel out the denominators} \\[1 em]2x+1 &= -9&& \text{ move 1 to the right } \\[1 em]2x &= -9-1&& \\[1 em]2x &= -10&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{10}{2}&& \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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