$$\frac{5}{2}x-14 = x+2$$

$$ \begin{aligned} \frac{5}{2}x-14 &= x+2&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{5}{2}x-2\cdot14 &= 2x+2\cdot2&& \text{cancel out the denominators} \\[1 em]5x-28 &= 2x+4&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -28 }$ to the right} \\[1 em]5x-2x &= 4+28&& \text{simplify left and right hand side} \\[1 em]3x &= 32&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{32}{3}&& \\[1 em] \end{aligned} $$

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