$$7x\cdot\frac{7}{7}+7-7 = 0$$

$$ \begin{aligned} 7x\cdot\frac{7}{7}+7-7 &= 0&& \text{multiply ALL terms by } \color{blue}{ 7 }. \\[1 em]77x\cdot\frac{7}{7}+7\cdot7-7\cdot7 &= 7\cdot0&& \text{cancel out the denominators} \\[1 em]49x+49-49 &= 0&& \text{simplify left side} \\[1 em]49x+49-49 &= 0&& \\[1 em]49x &= 0&& \text{ divide both sides by $ 49 $ } \\[1 em]x &= \frac{0}{49}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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