$$ \begin{aligned} x-13 &= 7(x+2)-4(x-7)&& \text{simplify right side} \\[1 em]x-13 &= 7x+14-(4x-28)&& \\[1 em]x-13 &= 7x+14-4x+28&& \\[1 em]x-13 &= 3x+42&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -13 }$ to the right} \\[1 em]x-3x &= 42+13&& \text{simplify left and right hand side} \\[1 em]-2x &= 55&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{55}{2}&& \\[1 em] \end{aligned} $$

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