$$ \begin{aligned} 2(x-5)+3 &= x+1&& \text{simplify left side} \\[1 em]2x-10+3 &= x+1&& \\[1 em]2x-7 &= x+1&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]2x-x &= 1+7&& \text{simplify left and right hand side} \\[1 em]x &= 8&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$
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