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

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