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 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 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 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.

1 answer

To analyze where Hank made a mistake in solving the equation \(25 = x^4 - 9\), let's go through the steps and check for errors.

The original equation is: \[ 25 = x^4 - 9 \]

Step 1: To get \(x^4\) by itself, we need to add 9 to both sides: \[ 25 + 9 = x^4 \] So, \[ 34 = x^4 \] (Hank made a mistake in this step; he wrote that \(16 = x^4\), which is incorrect.)

Step 2: To solve for \(x\), we need to take the fourth root of both sides: \[ x = \sqrt[4]{34} \] (Hank incorrectly stated \(x=64\). The operation he performed to get to \(64\) is not valid based on the correct calculation.)

Given this evaluation, Hank made a mistake in Step 1 when he incorrectly simplified \(25 + 9\) as \(16\) instead of \(34\).

Thus, 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.

Similar Questions
    1. answers icon 3 answers
  1. Hank's work to solve the equation 25=x/4−9is shown below. In which step did Hank make a mistake, and what mistake did he make?
    1. answers icon 1 answer
  2. Hank's work to solve the equation 25=x/4 − 9is shown below. In which step did Hank make a mistake, and what mistake did he
    1. answers icon 1 answer
  3. Hank's work to solve the equation 25=x4−9is shown below. In which step did Hank make a mistake, and what mistake did he make?
    1. answers icon 1 answer
more similar questions