$$ \begin{aligned} x+\frac{7}{9} &= 7&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9x+9\cdot\frac{7}{9} &= 9\cdot7&& \text{cancel out the denominators} \\[1 em]9x+7 &= 63&& \text{ move 7 to the right } \\[1 em]9x &= 63-7&& \\[1 em]9x &= 56&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{56}{9}&& \\[1 em] \end{aligned} $$

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