If Hill's second step is to divide both sides of the equation by 5, it implies that before this step he must have had an equation where the term involving \( x \) is multiplied by 5.
Let's check each response to see which one would require a division by 5 as an appropriate step:
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7 + x/5 = 22: In this equation, dividing both sides by 5 does not make sense, as \( x \) is already divided by 5.
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7 − x/5 = 22: In this equation, dividing by 5 does not apply as the term involving \( x \) is also divided.
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7 − 5x = 22: Rearranging this gives \( -5x = 22 - 7 \), which simplifies to \( -5x = 15 \). Dividing by \(-5\) would be a step, but not dividing by 5.
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7 + 5x = 22: Rearranging gives \( 5x = 22 - 7\) or \( 5x = 15\). Here, dividing both sides by 5 to solve for \( x \) is the correct next step, because you would get \( x = 3 \) after the division.
Thus, the equation Hill is solving is:
7 + 5x = 22
1 answer