$$ \begin{aligned} 3(x+1) &= 5(x-2)+7&& \text{simplify left and right hand side} \\[1 em]3x+3 &= 5x-10+7&& \\[1 em]3x+3 &= 5x-3&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]3x-5x &= -3-3&& \text{simplify left and right hand side} \\[1 em]-2x &= -6&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-6}{-2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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