$$ \begin{aligned} 5(x-2)+3 &= 2x+7&& \text{simplify left side} \\[1 em]5x-10+3 &= 2x+7&& \\[1 em]5x-7 &= 2x+7&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]5x-2x &= 7+7&& \text{simplify left and right hand side} \\[1 em]3x &= 14&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{14}{3}&& \\[1 em] \end{aligned} $$

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