$$ \begin{aligned} 5r-\frac{11}{8} &= \frac{9}{8}r\cdot\frac{21}{4}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot5r-8\cdot\frac{11}{8} &= 8 \cdot \frac{9}{8}r\cdot\frac{21}{4}&& \text{cancel out the denominators} \\[1 em]40r-11 &= \frac{189r}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot40r-4\cdot11 &= 4 \cdot \frac{189r}{4}&& \text{cancel out the denominators} \\[1 em]160r-44 &= 189r&& \text{move the $ \color{blue}{ 189r } $ to the left side and $ \color{blue}{ -44 }$ to the right} \\[1 em]160r-189r &= 44&& \text{simplify left side} \\[1 em]-29r &= 44&& \text{ divide both sides by $ -29 $ } \\[1 em]r &= -\frac{44}{29}&& \\[1 em] \end{aligned} $$

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