$$ \begin{aligned} -\frac{1}{10}x+5 &= 12&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]-10 \cdot \frac{1}{10}x+10\cdot5 &= 10\cdot12&& \text{cancel out the denominators} \\[1 em]-x+50 &= 120&& \text{ move 50 to the right } \\[1 em]-x &= 120-50&& \\[1 em]-x &= 70&& \text{switch signs on both sides} \\[1 em]x &= -70&& \\[1 em] \end{aligned} $$

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