$$ \begin{aligned} \frac{1}{4}(x+10) &= 2+\frac{1}{2}(x-1)&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}(x+10) &= 4\cdot2+4 \cdot \frac{1}{2}(x-1)&& \text{cancel out the denominators} \\[1 em]x+10 &= 8+2x-2&& \text{simplify right side} \\[1 em]x+10 &= 2x+6&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]x-2x &= 6-10&& \text{simplify left and right hand side} \\[1 em]-x &= -4&& \text{switch signs on both sides} \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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