$$\frac{2}{3}x-\frac{7}{6} = \frac{1}{6}x$$

$$ \begin{aligned} \frac{2}{3}x-\frac{7}{6} &= \frac{1}{6}x&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2}{3}x-6\cdot\frac{7}{6} &= 6 \cdot \frac{1}{6}x&& \text{cancel out the denominators} \\[1 em]4x-7 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]4x-x &= 7&& \text{simplify left side} \\[1 em]3x &= 7&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{7}{3}&& \\[1 em] \end{aligned} $$

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