$$\frac{1}{2} = \frac{x-2}{6}+1$$

$$ \begin{aligned} \frac{1}{2} &= \frac{x-2}{6}+1&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot\frac{1}{2} &= 6 \cdot \frac{x-2}{6}+6\cdot1&& \text{cancel out the denominators} \\[1 em]3 &= x-2+6&& \text{simplify right side} \\[1 em]3 &= x+4&& \text{ swap the left and right side of the equation } \\[1 em]x+4 &= 3&& \text{ move 4 to the right } \\[1 em]x &= 3-4&& \\[1 em]x &= -1&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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