To analyze Hank's work, let's take a closer look at the steps he provided to solve the equation \( 25 = x^4 - 9 \).
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Starting with the original equation: \[ 25 = x^4 - 9 \]
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In his Step 1, Hank claims to have simplified this to: \[ 16 = x^4 \] However, to go from \( 25 = x^4 - 9 \) to an equivalent equation, you should add 9 to both sides of the equation, not subtract it. The correct first step would be: \[ 25 + 9 = x^4 \] or \[ 34 = x^4 \]
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In Step 2, Hank then solves for \( x \): \[ x = 64 \] This would be correct if \( x^4 \) were 64, but since he made a mistake in Step 1, the value of \( x \) is also incorrect.
Given this analysis, the mistake is in Step 1. The first step needed to solve this correctly would be to add 9 to both sides of the equation, but Hank subtracted 9 instead.
Therefore, the correct response is: Hank made a mistake in Step 1. The first step needed to solve this correctly would be to add 9 to both sides of the equation. Hank subtracted 9 instead of adding 9.