$$ \begin{aligned} 4(x-3)+5 &= 2x+13&& \text{simplify left side} \\[1 em]4x-12+5 &= 2x+13&& \\[1 em]4x-7 &= 2x+13&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]4x-2x &= 13+7&& \text{simplify left and right hand side} \\[1 em]2x &= 20&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{20}{2}&& \\[1 em]x &= 10&& \\[1 em] \end{aligned} $$

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