$$ \begin{aligned} 10-2(x+3) &= 3x+2&& \text{simplify left side} \\[1 em]10-(2x+6) &= 3x+2&& \\[1 em]10-2x-6 &= 3x+2&& \\[1 em]-2x+4 &= 3x+2&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]-2x-3x &= 2-4&& \text{simplify left and right hand side} \\[1 em]-5x &= -2&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-2}{-5}&& \\[1 em]x &= \frac{2}{5}&& \\[1 em] \end{aligned} $$

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