Hank's work to solve the equation 25=x4−9

is shown below. In which step did Hank make a mistake, and what mistake did he make?

25=x4−9

Step 1: 16=x4

Step 2: x=64
(1 point)
Responses

Hank made a mistake in Step 2. The second step needed to solve this correctly would be to divide both sides of the equation by 4. Hank multiplied by 4 instead of dividing.
Hank made a mistake in Step 2. The second step needed to solve this correctly would be to divide both sides of the equation by 4. Hank multiplied by 4 instead of dividing.

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.
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.

Hank made a mistake in Step 2. The second step needed to solve this correctly would be to subtract 9 to both sides of the equation. Hank added 9 instead of subtracting 9.
Hank made a mistake in Step 2. The second step needed to solve this correctly would be to subtract 9 to both sides of the equation. Hank added 9 instead of subtracting 9.

Hank made a mistake in Step 1. The first step needed to solve this correctly would be to multiply both sides of the equation by 4. Hank divided by 4 instead of multiplying.

1 answer

To analyze Hank's work, let's take a closer look at the steps he provided to solve the equation \( 25 = x^4 - 9 \).

  1. Starting with the original equation: \[ 25 = x^4 - 9 \]

  2. 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 \[ 34 = x^4 \]

  3. 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.