$$ \begin{aligned} 4x+14+8x+7 &= 13x+12&& \text{simplify left side} \\[1 em]12x+21 &= 13x+12&& \text{move the $ \color{blue}{ 13x } $ to the left side and $ \color{blue}{ 21 }$ to the right} \\[1 em]12x-13x &= 12-21&& \text{simplify left and right hand side} \\[1 em]-x &= -9&& \text{switch signs on both sides} \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$

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