Question
$$4(x-8) = -32+4x$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 4(x-8) &= -32+4x&& \text{simplify left and right hand side} \\[1 em]4x-32 &= 4x-32&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -32 }$ to the right} \\[1 em]4x-4x &= -32+32&& \text{simplify left and right hand side} \\[1 em]4x-4x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
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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