$$ \begin{aligned} 4 \cdot \frac{r}{5}-\frac{r}{10} &= 7&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot4 \cdot \frac{r}{5}-10\frac{r}{10} &= 10\cdot7&& \text{cancel out the denominators} \\[1 em]8r-r &= 70&& \text{simplify left side} \\[1 em]7r &= 70&& \text{ divide both sides by $ 7 $ } \\[1 em]r &= \frac{70}{7}&& \\[1 em]r &= 10&& \\[1 em] \end{aligned} $$

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