$$ \begin{aligned} \frac{1}{2}x-\frac{16}{5} &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{1}{2}x-30\cdot\frac{16}{5} &= 30\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]15x-96 &= 10&& \text{ move -96 to the right } \\[1 em]15x &= 10+96&& \\[1 em]15x &= 106&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{106}{15}&& \\[1 em] \end{aligned} $$

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