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

Question

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 multiply both sides of the equation by 4. Hank divided by 4 instead of multiplying.
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.

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 add 9 to both sides of the equation. Hank subtracted 9 instead of adding 9.

Answer 1

To analyze Hank's work on the equation \(25 = x^4 - 9\):

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

2. To isolate \(x^4\), we should first add 9 to both sides: \[ 25 + 9 = x^4 \] This simplifies to: \[ 34 = x^4 \]

3. Once we have \(x^4 = 34\), we can then take the fourth root of both sides to find \(x\).

Hank wrote:

• Step 1: \(16 = x^4\) (this is incorrect)
• Step 2: \(x = 64\) (this is also incorrect)

Identifying the Mistake:

Hank made a mistake in Step 1. He incorrectly claimed that \(25 + 9 = x^4\) should yield \(x^4 = 16\) instead of \(x^4 = 34\).

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.