$$ \begin{aligned} 3(2x-1)+x &= 5x+3&& \text{simplify left side} \\[1 em]6x-3+x &= 5x+3&& \\[1 em]7x-3 &= 5x+3&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]7x-5x &= 3+3&& \text{simplify left and right hand side} \\[1 em]2x &= 6&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{6}{2}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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