$$ \begin{aligned} x-2 &= 2x+1&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]x-2x &= 1+2&& \text{simplify left and right hand side} \\[1 em]-x &= 3&& \text{switch signs on both sides} \\[1 em]x &= -3&& \\[1 em] \end{aligned} $$