Question
$$2x+4 = 5(x+1)-3(x+2)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2x+4 &= 5(x+1)-3(x+2)&& \text{simplify right side} \\[1 em]2x+4 &= 5x+5-(3x+6)&& \\[1 em]2x+4 &= 5x+5-3x-6&& \\[1 em]2x+4 &= 2x-1&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]2x-2x &= -1-4&& \text{simplify left and right hand side} \\[1 em]2x-2x &= -5&& \\[1 em]0 &= -5&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -5 } $ is FALSE, we conclude that the equation has no solution.
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