$$ \begin{aligned} \frac{3}{4}x+5 &= \frac{1}{2}(x-2)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{4}x+4\cdot5 &= 4 \cdot \frac{1}{2}(x-2)&& \text{cancel out the denominators} \\[1 em]3x+20 &= 2x-4&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]3x-2x &= -4-20&& \text{simplify left and right hand side} \\[1 em]x &= -24&& \\[1 em]x &= -24&& \\[1 em] \end{aligned} $$

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