Question
$$3\cdot(2+u)-u = 4+2(u+1)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 3\cdot(2+u)-u &= 4+2(u+1)&& \text{simplify left and right hand side} \\[1 em]6+3u-u &= 4+2u+2&& \\[1 em]2u+6 &= 2u+6&& \text{move the $ \color{blue}{ 2u } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]2u-2u &= 6-6&& \text{simplify left and right hand side} \\[1 em]2u-2u &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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