$$ \begin{aligned} 5x+\frac{7}{3^2} &= 3&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot5x+9\cdot\frac{7}{3^2} &= 9\cdot3&& \text{cancel out the denominators} \\[1 em]45x+7 &= 27&& \text{ move 7 to the right } \\[1 em]45x &= 27-7&& \\[1 em]45x &= 20&& \text{ divide both sides by $ 45 $ } \\[1 em]x &= \frac{20}{45}&& \\[1 em]x &= \frac{4}{9}&& \\[1 em] \end{aligned} $$

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