$$ \begin{aligned} -\frac{7}{4}-x+\frac{31}{10} &= -\frac{73}{20}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]-20\cdot\frac{7}{4}-20x+20\cdot\frac{31}{10} &= -20\cdot\frac{73}{20}&& \text{cancel out the denominators} \\[1 em]-35-20x+62 &= -73&& \text{simplify left side} \\[1 em]-20x+27 &= -73&& \text{ move 27 to the right } \\[1 em]-20x &= -73-27&& \\[1 em]-20x &= -100&& \text{ divide both sides by $ -20 $ } \\[1 em]x &= \frac{-100}{-20}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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