$$ \begin{aligned} \frac{5}{7}(x-9) &= 25&& \text{simplify left side} \\[1 em]\frac{5x-45}{7} &= 25&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{5x-45}{7} &= 7\cdot25&& \text{cancel out the denominators} \\[1 em]5x-45 &= 175&& \text{ move -45 to the right } \\[1 em]5x &= 175+45&& \\[1 em]5x &= 220&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{220}{5}&& \\[1 em]x &= 44&& \\[1 em] \end{aligned} $$

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