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)
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 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.

1 answer

Let's analyze Hank's work step by step.

The original equation is:

\[ 25 = x^4 - 9 \]

Step 1: Hank indicates that he moved to:

\[ 16 = x^4 \]

To check this, we should add 9 to both sides of the equation to isolate \(x^4\):

\[ 25 + 9 = x^4 \]

This simplifies to:

\[ 34 = x^4 \]

So, Hank made a mistake in Step 1. He incorrectly subtracted 9 instead of adding 9.

Step 2: In his work, Hank then solved for \(x\) by stating:

\[ x = 64 \]

This is incorrect because the previous result of \(x^4\) was incorrect. From the correct equation \(34 = x^4\), he should take the fourth root of \(34\) to find \(x\).

Thus, the correct identification of Hank's mistake 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.

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