$$ \begin{aligned} 7(-7x-1) &= -5(5x-8)&& \text{simplify left and right hand side} \\[1 em]-49x-7 &= -(25x-40)&& \\[1 em]-49x-7 &= -25x+40&& \text{move the $ \color{blue}{ -25x } $ to the left side and $ \color{blue}{ -7 }$ to the right} \\[1 em]-49x+25x &= 40+7&& \text{simplify left and right hand side} \\[1 em]-24x &= 47&& \text{ divide both sides by $ -24 $ } \\[1 em]x &= -\frac{47}{24}&& \\[1 em] \end{aligned} $$

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