$$ \begin{aligned} 12 &= x+\frac{4}{9}&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot12 &= 9x+9\cdot\frac{4}{9}&& \text{cancel out the denominators} \\[1 em]108 &= 9x+4&& \text{ swap the left and right side of the equation } \\[1 em]9x+4 &= 108&& \text{ move 4 to the right } \\[1 em]9x &= 108-4&& \\[1 em]9x &= 104&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{104}{9}&& \\[1 em] \end{aligned} $$

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