$$\frac{x}{5}+x = \frac{9}{10}$$

$$ \begin{aligned} \frac{x}{5}+x &= \frac{9}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10 \cdot \frac{x}{5}+10x &= 10\cdot\frac{9}{10}&& \text{cancel out the denominators} \\[1 em]2x+10x &= 9&& \text{simplify left side} \\[1 em]12x &= 9&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{9}{12}&& \\[1 em]x &= \frac{3}{4}&& \\[1 em] \end{aligned} $$

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