$$ \begin{aligned} \frac{x}{3}+\frac{x}{8} &= \frac{11}{24}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24 \cdot \frac{x}{3}+24\frac{x}{8} &= 24\cdot\frac{11}{24}&& \text{cancel out the denominators} \\[1 em]8x+3x &= 11&& \text{simplify left side} \\[1 em]11x &= 11&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{11}{11}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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