$$ \begin{aligned} 2+\frac{x}{2}+x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot2+2 \cdot \frac{x}{2}+2x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]4+x+2x &= 0&& \text{simplify left side} \\[1 em]3x+4 &= 0&& \text{ move the constants to the right } \\[1 em]3x &= -4&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{4}{3}&& \\[1 em] \end{aligned} $$

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