$$ \begin{aligned} 3(x-2)+2x &= 4x+1&& \text{simplify left side} \\[1 em]3x-6+2x &= 4x+1&& \\[1 em]5x-6 &= 4x+1&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]5x-4x &= 1+6&& \text{simplify left and right hand side} \\[1 em]x &= 7&& \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$
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