Question
$$4x-1 = 3(x+1)+x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4x-1 &= 3(x+1)+x&& \text{simplify right side} \\[1 em]4x-1 &= 3x+3+x&& \\[1 em]4x-1 &= 4x+3&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -1 }$ to the right} \\[1 em]4x-4x &= 3+1&& \text{simplify left and right hand side} \\[1 em]4x-4x &= 4&& \\[1 em]0 &= 4&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 4 } $ is FALSE, we conclude that the equation has no solution.
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