$$1+\frac{2}{3}x\cdot3 = 0$$

$$ \begin{aligned} 1+\frac{2}{3}x\cdot3 &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot1+3 \cdot \frac{2}{3}x\cdot3 &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]3+6x &= 0&& \text{ move the constants to the right } \\[1 em]6x &= -3&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{3}{6}&& \\[1 em]x &= -\frac{1}{2}&& \\[1 em] \end{aligned} $$

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