$$ \begin{aligned} x+\frac{x}{10} &= 4119+\frac{21}{50}&& \text{multiply ALL terms by } \color{blue}{ 50 }. \\[1 em]50x+50 \cdot \frac{x}{10} &= 50\cdot4119+50\cdot\frac{21}{50}&& \text{cancel out the denominators} \\[1 em]50x+5x &= 205950+21&& \text{simplify left and right hand side} \\[1 em]55x &= 205971&& \text{ divide both sides by $ 55 $ } \\[1 em]x &= \frac{205971}{55}&& \\[1 em] \end{aligned} $$

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