Question
$$3x+7 = 2(x+1)+x-5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3x+7 &= 2(x+1)+x-5&& \text{simplify right side} \\[1 em]3x+7 &= 2x+2+x-5&& \\[1 em]3x+7 &= 3x-3&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]3x-3x &= -3-7&& \text{simplify left and right hand side} \\[1 em]3x-3x &= -10&& \\[1 em]0 &= -10&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -10 } $ is FALSE, we conclude that the equation has no solution.
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