To determine which equation Hill is solving, we need to identify the situation where dividing both sides by 5 is a meaningful operation.
Let's analyze each option:
-
\(7 - \frac{x}{5} = 22\): If we were to multiply both sides by 5 first, we would get \(5(7 - \frac{x}{5}) = 5(22)\), leading to \(35 - x = 110\). This does not involve a direct division by 5 after simplifying, so it doesn't match Hill's step.
-
\(7 - 5x = 22\): Dividing both sides by 5 in this equation doesn't seem sensible or applicable either, as \(5x\) would need to be isolated first.
-
\(7 + \frac{x}{5} = 22\): If we subtract 7 from both sides, we would get \(\frac{x}{5} = 15\). Dividing both sides by 5 afterward would involve multiplying both sides by 5 first, leading us back to isolating \(x\). So if Hill divided first, it doesn't hold up here.
-
\(7 + 5x = 22\): If we subtract 7 from both sides, we find \(5x = 15\), and dividing both sides by 5 yields \(x = 3\).
In the context of the question, the only equation where dividing both sides by 5 would make sense as the second step is:
\(7 + 5x = 22\), after isolating \(5x\) first.
Thus, the original equation Hill is solving is:
\(7 + 5x = 22\).
1 answer