$$ \begin{aligned} \frac{34}{x} &= -\frac{17}{2}&& \text{multiply ALL terms by } \color{blue}{ x\cdot2 }. \\[1 em]x\cdot2\cdot\frac{34}{x} &= -x\cdot2\cdot\frac{17}{2}&& \text{cancel out the denominators} \\[1 em]68 &= -17x&& \text{ swap the left and right side of the equation } \\[1 em]-17x &= 68&& \text{ divide both sides by $ -17 $ } \\[1 em]x &= -\frac{68}{17}&& \\[1 em]x &= -4&& \\[1 em] \end{aligned} $$

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