$$ \begin{aligned} 2x+3 &= 3-\frac{x}{4}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot2x+4\cdot3 &= 4\cdot3-4 \cdot \frac{x}{4}&& \text{cancel out the denominators} \\[1 em]8x+12 &= 12-x&& \text{move the $ \color{blue}{ -x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]8x+x &= 12-12&& \text{simplify left and right hand side} \\[1 em]9x &= 0&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{0}{9}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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