$$ \begin{aligned} 3 &= \frac{z}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot3 &= 10 \cdot \frac{z}{10}&& \text{cancel out the denominators} \\[1 em]30 &= z&& \text{ swap the left and right side of the equation } \\[1 em]z &= 30&& \\[1 em]z &= 30&& \\[1 em] \end{aligned} $$
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