$$ \begin{aligned} 2(2x-3)+3 &= 2(x+5)&& \text{simplify left and right hand side} \\[1 em]4x-6+3 &= 2x+10&& \\[1 em]4x-3 &= 2x+10&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]4x-2x &= 10+3&& \text{simplify left and right hand side} \\[1 em]2x &= 13&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{13}{2}&& \\[1 em] \end{aligned} $$

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