$$2(x+3)-5 = 3x+1$$

$$ \begin{aligned} 2(x+3)-5 &= 3x+1&& \text{simplify left side} \\[1 em]2x+6-5 &= 3x+1&& \\[1 em]2x+1 &= 3x+1&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]2x-3x &= 1-1&& \text{simplify left and right hand side} \\[1 em]-x &= 0&& \text{ divide both sides by $ -1 $ } \\[1 em]x &= \frac{0}{-1}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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