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Hank's work to solve the equation 25=x4−925=x4−9 is shown below. In which step did Hank make a mistake, and what mistake did he...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 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 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.
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 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 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.
Answers
Answer
are you sure
Answer
its actually x/4
Answer
no its x divided by 4 you bot
Answer
which step is step 1
Answered by
GPT-4o mini
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.
Here's a breakdown of the correct solution:
Starting with the equation:
\[ 25 = x^4 - 9 \]
**Step 1:** To isolate \( x^4 \), add 9 to both sides:
\[ 25 + 9 = x^4 \]
\[ 34 = x^4 \]
**Step 2:** Now take the fourth root of both sides:
\[ x = \sqrt[4]{34} \]
In Hank’s work, he incorrectly concluded \( 16 = x^4 \) instead of \( 34 = x^4 \), leading to the wrong value for \( x \).
Here's a breakdown of the correct solution:
Starting with the equation:
\[ 25 = x^4 - 9 \]
**Step 1:** To isolate \( x^4 \), add 9 to both sides:
\[ 25 + 9 = x^4 \]
\[ 34 = x^4 \]
**Step 2:** Now take the fourth root of both sides:
\[ x = \sqrt[4]{34} \]
In Hank’s work, he incorrectly concluded \( 16 = x^4 \) instead of \( 34 = x^4 \), leading to the wrong value for \( x \).
Answered by
GPT-4o mini
Yes, let's go through the reasoning again carefully to confirm.
The original equation is:
\[ 25 = x^4 - 9 \]
To solve for \( x \):
**Step 1:** Add \( 9 \) to both sides, instead of subtracting:
\[
25 + 9 = x^4
\]
This gives:
\[
34 = x^4
\]
So Hank's mistake is in Step 1 where he incorrectly subtracted \( 9 \) instead of adding \( 9 \) to both sides.
**Step 2:** After correctly obtaining \( 34 = x^4 \), you would find \( x \) by taking the fourth root:
\[
x = \sqrt[4]{34}
\]
In Step 2, Hank wrote \( x = 64 \), which is not correct given his previous mistake.
Therefore, the statement is accurate: Hank made a mistake in Step 1 by subtracting \( 9 \) instead of adding it to both sides.
So, the correct answer 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:
\[ 25 = x^4 - 9 \]
To solve for \( x \):
**Step 1:** Add \( 9 \) to both sides, instead of subtracting:
\[
25 + 9 = x^4
\]
This gives:
\[
34 = x^4
\]
So Hank's mistake is in Step 1 where he incorrectly subtracted \( 9 \) instead of adding \( 9 \) to both sides.
**Step 2:** After correctly obtaining \( 34 = x^4 \), you would find \( x \) by taking the fourth root:
\[
x = \sqrt[4]{34}
\]
In Step 2, Hank wrote \( x = 64 \), which is not correct given his previous mistake.
Therefore, the statement is accurate: Hank made a mistake in Step 1 by subtracting \( 9 \) instead of adding it to both sides.
So, the correct answer 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.**
Answered by
GPT-4o mini
I apologize for any confusion in my previous response. Let's clarify Hank's work step-by-step with the given equation and identify where the mistake was made based on your comments.
Starting with the equation:
\[ 25 = x^4 - 9 \]
### To solve:
**Step 1:** Add \( 9 \) to both sides:
\[
25 + 9 = x^4
\]
\[
34 = x^4
\]
**Step 2:** Now solve for \( x \) by taking the fourth root:
\[
x = \sqrt[4]{34}
\]
It seems like there might be a misunderstanding in communicating the mistake related to \(x^4\) initially. To clarify, it appears you wanted to reference a division by 4 later.
However, based on Hank's progression:
- In Step 1, Hank's error is going from the original equation to \( 16 = x^4 \), which should be \( 34 = x^4 \) instead.
- In Step 2, after incorrectly stating \( x^4 = 16 \), Hank further made an error by concluding \( x = 64 \) instead of correctly taking the fourth root of \(34\).
So, if your mention of "x/4" relates to the next logical step (dividing by 4) after setting up \(x^4\), it might seem to reference an incorrect approach to isolating \(x\).
In summary, the key mistakes Hank made were:
1. The misstep in Step 1 where he didn't add 9 properly.
2. The incorrect conclusion in Step 2.
Would you clarify what you meant about "x/4"? This will help me provide the most accurate support!
Starting with the equation:
\[ 25 = x^4 - 9 \]
### To solve:
**Step 1:** Add \( 9 \) to both sides:
\[
25 + 9 = x^4
\]
\[
34 = x^4
\]
**Step 2:** Now solve for \( x \) by taking the fourth root:
\[
x = \sqrt[4]{34}
\]
It seems like there might be a misunderstanding in communicating the mistake related to \(x^4\) initially. To clarify, it appears you wanted to reference a division by 4 later.
However, based on Hank's progression:
- In Step 1, Hank's error is going from the original equation to \( 16 = x^4 \), which should be \( 34 = x^4 \) instead.
- In Step 2, after incorrectly stating \( x^4 = 16 \), Hank further made an error by concluding \( x = 64 \) instead of correctly taking the fourth root of \(34\).
So, if your mention of "x/4" relates to the next logical step (dividing by 4) after setting up \(x^4\), it might seem to reference an incorrect approach to isolating \(x\).
In summary, the key mistakes Hank made were:
1. The misstep in Step 1 where he didn't add 9 properly.
2. The incorrect conclusion in Step 2.
Would you clarify what you meant about "x/4"? This will help me provide the most accurate support!
Answered by
GPT-4o mini
I apologize for any confusion in our conversation. Let me clarify further and examine Hank's steps again.
The original equation is:
\[ 25 = x^4 - 9 \]
### Correct Steps for Solving the Equation:
1. **Add 9 to both sides**:
\[
25 + 9 = x^4
\]
This simplifies to:
\[
34 = x^4
\]
2. **Then, take the fourth root of both sides** to solve for \(x\):
\[
x = \sqrt[4]{34}
\]
**Hank's Steps:**
1. Hank went from \( 25 = x^4 - 9 \) to \( 16 = x^4 \) incorrectly. This was his first mistake; he should have added 9 to get 34.
2. From \( 16 = x^4 \), Hank incorrectly calculated that \( x = 64 \).
### Summary of Mistakes:
- **Step 1:** Hank should have added 9 instead of arriving at 16.
- **Step 2:** He incorrectly concluded the value for \( x \) based on the incorrect equation.
Now, regarding your reference to **"x divided by 4"**:
If you were referring to the misunderstanding of isolating the variable \( x \) in the context of its exponent rather than the arithmetic I initially laid out, I might have misunderstood our exchange. Hank never actually divided by 4—he miscalculated.
So, to clarify:
- **Hank made an error in Step 1**: he should have added, not subtracted, leading to the wrong statement.
- The idea of dividing does not also apply as he should have been focused on determining \( x \) correctly.
Please let me know if this addresses your concerns or if I can assist further! Thank you for your patience.
The original equation is:
\[ 25 = x^4 - 9 \]
### Correct Steps for Solving the Equation:
1. **Add 9 to both sides**:
\[
25 + 9 = x^4
\]
This simplifies to:
\[
34 = x^4
\]
2. **Then, take the fourth root of both sides** to solve for \(x\):
\[
x = \sqrt[4]{34}
\]
**Hank's Steps:**
1. Hank went from \( 25 = x^4 - 9 \) to \( 16 = x^4 \) incorrectly. This was his first mistake; he should have added 9 to get 34.
2. From \( 16 = x^4 \), Hank incorrectly calculated that \( x = 64 \).
### Summary of Mistakes:
- **Step 1:** Hank should have added 9 instead of arriving at 16.
- **Step 2:** He incorrectly concluded the value for \( x \) based on the incorrect equation.
Now, regarding your reference to **"x divided by 4"**:
If you were referring to the misunderstanding of isolating the variable \( x \) in the context of its exponent rather than the arithmetic I initially laid out, I might have misunderstood our exchange. Hank never actually divided by 4—he miscalculated.
So, to clarify:
- **Hank made an error in Step 1**: he should have added, not subtracted, leading to the wrong statement.
- The idea of dividing does not also apply as he should have been focused on determining \( x \) correctly.
Please let me know if this addresses your concerns or if I can assist further! Thank you for your patience.
Answered by
GPT-4o mini
Let's clarify the steps based on the given equation, starting from the beginning. Here’s Hank’s original equation and the steps he took:
### Original Equation:
\[ 25 = x^4 - 9 \]
### Hank’s Steps:
1. **Step 1:** Hank wrote \( 16 = x^4 \).
2. **Step 2:** Hank concluded \( x = 64 \).
### Analyzing the Steps:
- **Step 1 (Hank’s work):** The equation should have been manipulated to read \( 34 = x^4 \) instead of \( 16 = x^4 \). This is **where Hank made his mistake**. He needed to add 9 to both sides, not derive \( 16 \).
- **Correct Step 1:**
\[
25 + 9 = x^4
\]
Which correctly gives:
\[
34 = x^4
\]
- **Step 2 (Hank’s work):** Since Step 1 was incorrect, his calculation in Step 2 (arriving at \( x = 64 \)) also becomes invalid.
### Conclusion:
Hank made a mistake in **Step 1** where he incorrectly assessed \( 16 = x^4 \). The valid first step should have reinforced addition of 9 to arrive at \( 34 = x^4 \).
Thank you for your patience, and I hope this clearly outlines where the mistake lies. If you have further questions or discussions, feel free to ask!
### Original Equation:
\[ 25 = x^4 - 9 \]
### Hank’s Steps:
1. **Step 1:** Hank wrote \( 16 = x^4 \).
2. **Step 2:** Hank concluded \( x = 64 \).
### Analyzing the Steps:
- **Step 1 (Hank’s work):** The equation should have been manipulated to read \( 34 = x^4 \) instead of \( 16 = x^4 \). This is **where Hank made his mistake**. He needed to add 9 to both sides, not derive \( 16 \).
- **Correct Step 1:**
\[
25 + 9 = x^4
\]
Which correctly gives:
\[
34 = x^4
\]
- **Step 2 (Hank’s work):** Since Step 1 was incorrect, his calculation in Step 2 (arriving at \( x = 64 \)) also becomes invalid.
### Conclusion:
Hank made a mistake in **Step 1** where he incorrectly assessed \( 16 = x^4 \). The valid first step should have reinforced addition of 9 to arrive at \( 34 = x^4 \).
Thank you for your patience, and I hope this clearly outlines where the mistake lies. If you have further questions or discussions, feel free to ask!
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