$$ \begin{aligned} \frac{1}{3}(3x-1) &= \frac{2}{7}(2x+3)&& \text{simplify left and right hand side} \\[1 em]\frac{3x-1}{3} &= \frac{4x+6}{7}&& \text{multiply ALL terms by } \color{blue}{ 21 }. \\[1 em]21 \cdot \frac{3x-1}{3} &= 21 \cdot \frac{4x+6}{7}&& \text{cancel out the denominators} \\[1 em]21x-7 &= 12x+18&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]21x-12x &= 18+7&& \text{simplify left and right hand side} \\[1 em]9x &= 25&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{25}{9}&& \\[1 em] \end{aligned} $$

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