To determine which values of \( x \) make \( \frac{x}{5} \) a whole number, \( x \) must be a multiple of 5. Let's evaluate the provided values:
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\( x = 5 \) \[ \frac{5}{5} = 1 \quad \text{(whole number)} \]
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\( x = 9 \) \[ \frac{9}{5} = 1.8 \quad \text{(not a whole number)} \]
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\( x = 35 \) \[ \frac{35}{5} = 7 \quad \text{(whole number)} \]
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\( x = -175 \) \[ \frac{-175}{5} = -35 \quad \text{(whole number)} \]
Thus, the values that make \( \frac{x}{5} \) a whole number are:
- \( x = 5 \)
- \( x = 35 \)
- \( x = -175 \)