$$ \begin{aligned} \frac{z}{3}-3 &= 1&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{z}{3}-3\cdot3 &= 3\cdot1&& \text{cancel out the denominators} \\[1 em]z-9 &= 3&& \text{ move -9 to the right } \\[1 em]z &= 3+9&& \\[1 em]z &= 12&& \\[1 em]z &= 12&& \\[1 em] \end{aligned} $$
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