Question
$$6\cdot\frac{3}{13}-3 = 7\cdot\frac{3}{13}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 6\cdot\frac{3}{13}-3 &= 7\cdot\frac{3}{13}&& \text{multiply ALL terms by } \color{blue}{ 13 }. \\[1 em]13\cdot6\cdot\frac{3}{13}-13\cdot3 &= 13\cdot7\cdot\frac{3}{13}&& \text{cancel out the denominators} \\[1 em]18-39 &= 21&& \text{simplify left side} \\[1 em]-21 &= 21&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -21 = 21 } $ is FALSE, we conclude that the equation has no solution.
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