$$ \begin{aligned} x+\frac{35}{100}x &= 22&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100x+100 \cdot \frac{35}{100}x &= 100\cdot22&& \text{cancel out the denominators} \\[1 em]100x+35x &= 2200&& \text{simplify left side} \\[1 em]135x &= 2200&& \text{ divide both sides by $ 135 $ } \\[1 em]x &= \frac{2200}{135}&& \\[1 em]x &= \frac{440}{27}&& \\[1 em] \end{aligned} $$

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