Question
$$3\cdot\frac{4}{5} = 5\cdot\frac{4}{5}-\frac{8}{5}$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 3\cdot\frac{4}{5} &= 5\cdot\frac{4}{5}-\frac{8}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5\cdot3\cdot\frac{4}{5} &= 5\cdot5\cdot\frac{4}{5}-5\cdot\frac{8}{5}&& \text{cancel out the denominators} \\[1 em]12 &= 20-8&& \text{simplify right side} \\[1 em]12 &= 12&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 12 = 12 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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