$$2 \cdot \frac{a}{3}+1 = 7 \cdot \frac{a}{15}+3$$

$$ \begin{aligned} 2 \cdot \frac{a}{3}+1 &= 7 \cdot \frac{a}{15}+3&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15\cdot2 \cdot \frac{a}{3}+15\cdot1 &= 15\cdot7 \cdot \frac{a}{15}+15\cdot3&& \text{cancel out the denominators} \\[1 em]10a+15 &= 7a+45&& \text{move the $ \color{blue}{ 7a } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]10a-7a &= 45-15&& \text{simplify left and right hand side} \\[1 em]3a &= 30&& \text{ divide both sides by $ 3 $ } \\[1 em]a &= \frac{30}{3}&& \\[1 em]a &= 10&& \\[1 em] \end{aligned} $$

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