Question
$$5 \cdot \frac{x}{x} = 5$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 5 \cdot \frac{x}{x} &= 5&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot5 \cdot \frac{x}{x} &= x\cdot5&& \text{cancel out the denominators} \\[1 em]5x &= 5x&& \text{move the $ \color{blue}{ 5x } $ to the left side} \\[1 em]5x-5x &= 0&& \text{simplify left side} \\[1 em]5x-5x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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