Question
$$-6(w-4)+8w = 2(w+9)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -6(w-4)+8w &= 2(w+9)&& \text{simplify left and right hand side} \\[1 em]-(6w-24)+8w &= 2w+18&& \\[1 em]-6w+24+8w &= 2w+18&& \\[1 em]2w+24 &= 2w+18&& \text{move the $ \color{blue}{ 2w } $ to the left side and $ \color{blue}{ 24 }$ to the right} \\[1 em]2w-2w &= 18-24&& \text{simplify left and right hand side} \\[1 em]2w-2w &= -6&& \\[1 em]0 &= -6&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -6 } $ is FALSE, we conclude that the equation has no solution.
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