$$ \begin{aligned} \frac{6}{5}x+16 &= \frac{24}{5}x-2&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{6}{5}x+5\cdot16 &= 5 \cdot \frac{24}{5}x-5\cdot2&& \text{cancel out the denominators} \\[1 em]6x+80 &= 24x-10&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ 80 }$ to the right} \\[1 em]6x-24x &= -10-80&& \text{simplify left and right hand side} \\[1 em]-18x &= -90&& \text{ divide both sides by $ -18 $ } \\[1 em]x &= \frac{-90}{-18}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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