$$ \begin{aligned} x+\frac{3}{2}+x &= 21&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2\cdot\frac{3}{2}+2x &= 2\cdot21&& \text{cancel out the denominators} \\[1 em]2x+3+2x &= 42&& \text{simplify left side} \\[1 em]4x+3 &= 42&& \text{ move 3 to the right } \\[1 em]4x &= 42-3&& \\[1 em]4x &= 39&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{39}{4}&& \\[1 em] \end{aligned} $$

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