$$4+x = 3+\frac{x}{2}$$

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

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