$$ \begin{aligned} -2k+\frac{28}{9} &= \frac{5}{3}k-5k&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]-9\cdot2k+9\cdot\frac{28}{9} &= 9 \cdot \frac{5}{3}k-9\cdot5k&& \text{cancel out the denominators} \\[1 em]-18k+28 &= 15k-45k&& \text{simplify right side} \\[1 em]-18k+28 &= -30k&& \text{move the $ \color{blue}{ -30k } $ to the left side and $ \color{blue}{ 28 }$ to the right} \\[1 em]-18k+30k &= -28&& \text{simplify left side} \\[1 em]12k &= -28&& \text{ divide both sides by $ 12 $ } \\[1 em]k &= -\frac{28}{12}&& \\[1 em]k &= -\frac{7}{3}&& \\[1 em] \end{aligned} $$

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