$$ \begin{aligned} \frac{653}{1000} &= 154000000x&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000\cdot\frac{653}{1000} &= 1000\cdot154000000x&& \text{cancel out the denominators} \\[1 em]653 &= 154000000000x&& \text{ swap the left and right side of the equation } \\[1 em]154000000000x &= 653&& \\[1 em]x &= 653&& \\[1 em] \end{aligned} $$
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