Question
$$2(x+4) = 4x-(2x+4)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2(x+4) &= 4x-(2x+4)&& \text{simplify left and right hand side} \\[1 em]2x+8 &= 4x-2x-4&& \\[1 em]2x+8 &= 2x-4&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]2x-2x &= -4-8&& \text{simplify left and right hand side} \\[1 em]2x-2x &= -12&& \\[1 em]0 &= -12&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -12 } $ is FALSE, we conclude that the equation has no solution.
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