Question
$$3\cdot\frac{2}{9}+\frac{1}{3} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3\cdot\frac{2}{9}+\frac{1}{3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9\cdot3\cdot\frac{2}{9}+9\cdot\frac{1}{3} &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]6+3 &= 0&& \text{simplify left side} \\[1 em]9 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 9 = 0 } $ is FALSE, we conclude that the equation has no solution.
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