$$\frac{t+9}{3} = \frac{t+10}{4}$$

$$ \begin{aligned} \frac{t+9}{3} &= \frac{t+10}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{t+9}{3} &= 12 \cdot \frac{t+10}{4}&& \text{cancel out the denominators} \\[1 em]4t+36 &= 3t+30&& \text{move the $ \color{blue}{ 3t } $ to the left side and $ \color{blue}{ 36 }$ to the right} \\[1 em]4t-3t &= 30-36&& \text{simplify left and right hand side} \\[1 em]t &= -6&& \\[1 em]t &= -6&& \\[1 em] \end{aligned} $$

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