$$ \begin{aligned} \frac{1}{2}\cdot4x+2\cdot2x-2 &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{1}{2}\cdot4x+22\cdot2x-2\cdot2 &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]4x+8x-4 &= 0&& \text{simplify left side} \\[1 em]12x-4 &= 0&& \text{ move the constants to the right } \\[1 em]12x &= 4&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{4}{12}&& \\[1 em]x &= \frac{1}{3}&& \\[1 em] \end{aligned} $$

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