$$ \begin{aligned} 40+4 \cdot \frac{m}{10} &= 100+5 \cdot \frac{m}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot40+10\cdot4 \cdot \frac{m}{10} &= 10\cdot100+10\cdot5 \cdot \frac{m}{10}&& \text{cancel out the denominators} \\[1 em]400+4m &= 1000+5m&& \text{move the $ \color{blue}{ 5m } $ to the left side and $ \color{blue}{ 400 }$ to the right} \\[1 em]4m-5m &= 1000-400&& \text{simplify left and right hand side} \\[1 em]-m &= 600&& \text{switch signs on both sides} \\[1 em]m &= -600&& \\[1 em] \end{aligned} $$

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