$$ \begin{aligned} 3+2(x-4) &= 5x+1&& \text{simplify left side} \\[1 em]3+2x-8 &= 5x+1&& \\[1 em]2x-5 &= 5x+1&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]2x-5x &= 1+5&& \text{simplify left and right hand side} \\[1 em]-3x &= 6&& \text{ divide both sides by $ -3 $ } \\[1 em]x &= -\frac{6}{3}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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