[math]\frac{8}{-4x}\neq -2, \frac{8}{-4x} = \frac{-2}{x}. \frac{-4x}{-4x}\neq x, \frac{-4x}{-4x}=1[/math]. You know that when you divide the same two expressions that you get 1, not x.
I would call the process solving a linear equation.
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