$$ \begin{aligned} \frac{3}{4}x-2 &= \frac{1}{2}x+7&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{3}{4}x-4\cdot2 &= 4 \cdot \frac{1}{2}x+4\cdot7&& \text{cancel out the denominators} \\[1 em]3x-8 &= 2x+28&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]3x-2x &= 28+8&& \text{simplify left and right hand side} \\[1 em]x &= 36&& \\[1 em]x &= 36&& \\[1 em] \end{aligned} $$

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