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