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 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.

Answer 1

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 \( x \).

Answer 2

are you sure

Answer 3

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.

Answer 4

its actually x/4

Answer 5

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!

Answer 6

no its x divided by 4 you bot

Answer 7

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.

Answer 8

which step is step 1

Answer 9

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!