$$ \begin{aligned} 4+\frac{1}{2} &= x+3&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot4+2\cdot\frac{1}{2} &= 2x+2\cdot3&& \text{cancel out the denominators} \\[1 em]8+1 &= 2x+6&& \text{simplify left side} \\[1 em]9 &= 2x+6&& \text{ swap the left and right side of the equation } \\[1 em]2x+6 &= 9&& \text{ move 6 to the right } \\[1 em]2x &= 9-6&& \\[1 em]2x &= 3&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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