$$ \begin{aligned} 6-\frac{3}{4}x+\frac{1}{3} &= \frac{1}{2}x+5&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot6-12 \cdot \frac{3}{4}x+12\cdot\frac{1}{3} &= 12 \cdot \frac{1}{2}x+12\cdot5&& \text{cancel out the denominators} \\[1 em]72-9x+4 &= 6x+60&& \text{simplify left side} \\[1 em]-9x+76 &= 6x+60&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 76 }$ to the right} \\[1 em]-9x-6x &= 60-76&& \text{simplify left and right hand side} \\[1 em]-15x &= -16&& \text{ divide both sides by $ -15 $ } \\[1 em]x &= \frac{-16}{-15}&& \\[1 em]x &= \frac{16}{15}&& \\[1 em] \end{aligned} $$

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