$$x-2(x+4) = 1+3(x+2)$$

$$ \begin{aligned} x-2(x+4) &= 1+3(x+2)&& \text{simplify left and right hand side} \\[1 em]x-(2x+8) &= 1+3x+6&& \\[1 em]x-2x-8 &= 3x+7&& \\[1 em]-x-8 &= 3x+7&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]-x-3x &= 7+8&& \text{simplify left and right hand side} \\[1 em]-4x &= 15&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{15}{4}&& \\[1 em] \end{aligned} $$

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