Question
$$-3x-1 = 8-3(x+2)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} -3x-1 &= 8-3(x+2)&& \text{simplify right side} \\[1 em]-3x-1 &= 8-(3x+6)&& \\[1 em]-3x-1 &= 8-3x-6&& \\[1 em]-3x-1 &= -3x+2&& \text{move the $ \color{blue}{ -3x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]-3x+3x &= 2+1&& \text{simplify left and right hand side} \\[1 em]-3x+3x &= 3&& \\[1 em]0 &= 3&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 3 } $ is FALSE, we conclude that the equation has no solution.
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