$$ \begin{aligned} x+\frac{1}{2}x+3 &= \frac{3}{8}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8x+8 \cdot \frac{1}{2}x+8\cdot3 &= 8\cdot\frac{3}{8}&& \text{cancel out the denominators} \\[1 em]8x+4x+24 &= 3&& \text{simplify left side} \\[1 em]12x+24 &= 3&& \text{ move 24 to the right } \\[1 em]12x &= 3-24&& \\[1 em]12x &= -21&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= -\frac{21}{12}&& \\[1 em]x &= -\frac{7}{4}&& \\[1 em] \end{aligned} $$

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