$$ \begin{aligned} \frac{3}{2}(x+5)-\frac{1}{4}(x+24) &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{2}(x+5)-4\frac{1}{4}(x+24) &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]6x+30-(x+24) &= 0&& \text{simplify left side} \\[1 em]6x+30-x-24 &= 0&& \\[1 em]5x+6 &= 0&& \text{ move the constants to the right } \\[1 em]5x &= -6&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= -\frac{6}{5}&& \\[1 em] \end{aligned} $$

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