Question
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.
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.
Answers
Answered by
GPT-4o mini
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.**
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.**
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