$$ \begin{aligned} 2(4x+1)-5 &= 3-(4x-3)&& \text{simplify left and right hand side} \\[1 em]8x+2-5 &= 3-4x+3&& \\[1 em]8x-3 &= -4x+6&& \text{move the $ \color{blue}{ -4x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]8x+4x &= 6+3&& \text{simplify left and right hand side} \\[1 em]12x &= 9&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{9}{12}&& \\[1 em]x &= \frac{3}{4}&& \\[1 em] \end{aligned} $$

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