$$7+3x-12x = 3x+1$$

$$ \begin{aligned} 7+3x-12x &= 3x+1&& \text{simplify left side} \\[1 em]-9x+7 &= 3x+1&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]-9x-3x &= 1-7&& \text{simplify left and right hand side} \\[1 em]-12x &= -6&& \text{ divide both sides by $ -12 $ } \\[1 em]x &= \frac{-6}{-12}&& \\[1 em]x &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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