$$ \begin{aligned} 8x-14 &= x-7&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -14 }$ to the right} \\[1 em]8x-x &= -7+14&& \text{simplify left and right hand side} \\[1 em]7x &= 7&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{7}{7}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$
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