$$ \begin{aligned} 3x+4(x+1) &= x+2(x+3)&& \text{simplify left and right hand side} \\[1 em]3x+4x+4 &= x+2x+6&& \\[1 em]7x+4 &= 3x+6&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]7x-3x &= 6-4&& \text{simplify left and right hand side} \\[1 em]4x &= 2&& \text{ divide both sides by $ 4 $ } \\[1 em]x &= \frac{2}{4}&& \\[1 em]x &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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