$$ \begin{aligned} \frac{2x+5}{4} &= \frac{2-3x}{2}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{2x+5}{4} &= 4 \cdot \frac{2-3x}{2}&& \text{cancel out the denominators} \\[1 em]2x+5 &= -6x+4&& \text{move the $ \color{blue}{ -6x } $ to the left side and $ \color{blue}{ 5 }$ to the right} \\[1 em]2x+6x &= 4-5&& \text{simplify left and right hand side} \\[1 em]8x &= -1&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= -\frac{1}{8}&& \\[1 em] \end{aligned} $$

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