$$ \begin{aligned} 8x-2 &= \frac{25}{4}x+26&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4\cdot8x-4\cdot2 &= 4 \cdot \frac{25}{4}x+4\cdot26&& \text{cancel out the denominators} \\[1 em]32x-8 &= 25x+104&& \text{move the $ \color{blue}{ 25x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]32x-25x &= 104+8&& \text{simplify left and right hand side} \\[1 em]7x &= 112&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{112}{7}&& \\[1 em]x &= 16&& \\[1 em] \end{aligned} $$

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