$$ \begin{aligned} 16-2t &= \frac{3}{2}t+9&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot16-2\cdot2t &= 2 \cdot \frac{3}{2}t+2\cdot9&& \text{cancel out the denominators} \\[1 em]32-4t &= 3t+18&& \text{move the $ \color{blue}{ 3t } $ to the left side and $ \color{blue}{ 32 }$ to the right} \\[1 em]-4t-3t &= 18-32&& \text{simplify left and right hand side} \\[1 em]-7t &= -14&& \text{ divide both sides by $ -7 $ } \\[1 em]t &= \frac{-14}{-7}&& \\[1 em]t &= 2&& \\[1 em] \end{aligned} $$

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