$$ \begin{aligned} 2x-\frac{3}{12}+x &= 2x+\frac{3}{2}+3&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot2x-12\cdot\frac{3}{12}+12x &= 12\cdot2x+12\cdot\frac{3}{2}+12\cdot3&& \text{cancel out the denominators} \\[1 em]24x-3+12x &= 24x+18+36&& \text{simplify left and right hand side} \\[1 em]36x-3 &= 24x+54&& \text{move the $ \color{blue}{ 24x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]36x-24x &= 54+3&& \text{simplify left and right hand side} \\[1 em]12x &= 57&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{57}{12}&& \\[1 em]x &= \frac{19}{4}&& \\[1 em] \end{aligned} $$

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