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