$$ \begin{aligned} \frac{1}{2}+\frac{3}{2}x+10 &= 15&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot\frac{1}{2}+2\frac{3}{2}x+2\cdot10 &= 2\cdot15&& \text{cancel out the denominators} \\[1 em]1+3x+20 &= 30&& \text{simplify left side} \\[1 em]3x+21 &= 30&& \text{ move 21 to the right } \\[1 em]3x &= 30-21&& \\[1 em]3x &= 9&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{9}{3}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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