To determine which equation Hill is solving based on his second step of dividing both sides by 5, we can analyze each option provided.
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\(7 - \frac{x}{5} = 22\): If Hill were to first isolate \(\frac{x}{5}\), he would have to subtract 7 from both sides first. After that, dividing by 5 does not directly apply.
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\(7 + 5x = 22\): In this equation, there is no element to divide by 5 that would lead to a simple equation on both sides after one step.
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\(7 - 5x = 22\): Similar to the second equation, there is no direct application of dividing both sides by 5.
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\(7 + \frac{x}{5} = 22\): First, if Hill subtracts 7 from both sides, he would get \(\frac{x}{5} = 15\). Then, to isolate \(x\), he would need to multiply both sides by 5. Therefore, he would not divide by 5 here either as a second step.
None of the equations would provide a situation where dividing by 5 would be the correct second step. However, if we consider typical algebraic manipulation involving fractions, the most likely candidate seems to be \(7 + \frac{x}{5} = 22\), where Hill might subtract 7 from both sides first (leading to \(\frac{x}{5} = 15\)) and then decide to divide both sides by 5 in an earlier manipulation.
Thus, the answer most consistent with the clue about dividing by 5 would be:
7 + \(\frac{x}{5} = 22\).