$$3(x-2) = \frac{x+3}{2}$$

$$ \begin{aligned} 3(x-2) &= \frac{x+3}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3(x-2) &= 2 \cdot \frac{x+3}{2}&& \text{cancel out the denominators} \\[1 em]6x-12 &= x+3&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]6x-x &= 3+12&& \text{simplify left and right hand side} \\[1 em]5x &= 15&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{15}{5}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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