Question
$$3x-2(x+1) = x+5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3x-2(x+1) &= x+5&& \text{simplify left side} \\[1 em]3x-(2x+2) &= x+5&& \\[1 em]3x-2x-2 &= x+5&& \\[1 em]x-2 &= x+5&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]x-x &= 5+2&& \text{simplify left and right hand side} \\[1 em]x-x &= 7&& \\[1 em]0 &= 7&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 7 } $ is FALSE, we conclude that the equation has no solution.
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