$$ \begin{aligned} 3x\cdot\frac{11}{2}+\frac{1}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]23x\cdot\frac{11}{2}+2\cdot\frac{1}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]33x+1 &= 0&& \text{ move the constants to the right } \\[1 em]33x &= -1&& \text{ divide both sides by $ 33 $ } \\[1 em]x &= -\frac{1}{33}&& \\[1 em] \end{aligned} $$

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