$$ \begin{aligned} \frac{4x-8}{2} &= \frac{3x+1}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{4x-8}{2} &= 6 \cdot \frac{3x+1}{3}&& \text{cancel out the denominators} \\[1 em]12x-24 &= 6x+2&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -24 }$ to the right} \\[1 em]12x-6x &= 2+24&& \text{simplify left and right hand side} \\[1 em]6x &= 26&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{26}{6}&& \\[1 em]x &= \frac{13}{3}&& \\[1 em] \end{aligned} $$

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