Question
$$4-\frac{16}{4}+2\cdot5-10 = 0$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 4-\frac{16}{4}+2\cdot5-10 &= 0&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot4-4\cdot\frac{16}{4}+4\cdot2\cdot5-4\cdot10 &= 4\cdot0&& \text{cancel out the denominators} \\[1 em]16-16+40-40 &= 0&& \text{simplify left side} \\[1 em]16-16+40-40 &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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