To determine which equation Hill is solving, we can analyze each option to see which one, when undergoing the second step of dividing both sides by 5, makes sense:
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7 - z/5 = 22:
- If we were to divide both sides by 5, we'd get: \[ \frac{7 - z/5}{5} = \frac{22}{5} \]
- This is not directly useful since the equation involves both addition and subtraction of z/5, and it does not simplify the variable.
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7 - 5x = 22:
- Dividing both sides by 5 gives: \[ \frac{7 - 5x}{5} = \frac{22}{5} \]
- This doesn't isolate x in a straightforward manner.
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7 + z/5 = 22:
- Dividing both sides by 5 gives: \[ \frac{7 + z/5}{5} = \frac{22}{5} \]
- This will not yield an obvious simplification for z.
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7 + 5x = 22:
- Dividing both sides by 5 gives: \[ \frac{7 + 5x}{5} = \frac{22}{5} \]
- This rearranges to: \[ \frac{7}{5} + x = \frac{22}{5} \]
- This effectively isolates x in the equation allowing for further steps.
From this analysis, it appears that the most straightforward equation that Hill is likely solving is 7 + 5x = 22 because dividing both sides by 5 leads to a simpler expression that can be further manipulated.