$$ \begin{aligned} -\frac{6}{5}k+9 &= \frac{5}{3}&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]-15 \cdot \frac{6}{5}k+15\cdot9 &= 15\cdot\frac{5}{3}&& \text{cancel out the denominators} \\[1 em]-18k+135 &= 25&& \text{ move 135 to the right } \\[1 em]-18k &= 25-135&& \\[1 em]-18k &= -110&& \text{ divide both sides by $ -18 $ } \\[1 em]k &= \frac{-110}{-18}&& \\[1 em]k &= \frac{55}{9}&& \\[1 em] \end{aligned} $$

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