$$\frac{5x-2}{3}+\frac{11}{4} = 0$$

$$ \begin{aligned} \frac{5x-2}{3}+\frac{11}{4} &= 0&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{5x-2}{3}+12\cdot\frac{11}{4} &= 12\cdot0&& \text{cancel out the denominators} \\[1 em]20x-8+33 &= 0&& \text{simplify left side} \\[1 em]20x+25 &= 0&& \text{ move the constants to the right } \\[1 em]20x &= -25&& \text{ divide both sides by $ 20 $ } \\[1 em]x &= -\frac{25}{20}&& \\[1 em]x &= -\frac{5}{4}&& \\[1 em] \end{aligned} $$

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