$$ \begin{aligned} \frac{x}{7}+x &= 19&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]7 \cdot \frac{x}{7}+7x &= 7\cdot19&& \text{cancel out the denominators} \\[1 em]x+7x &= 133&& \text{simplify left side} \\[1 em]8x &= 133&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= \frac{133}{8}&& \\[1 em] \end{aligned} $$
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