Question
Hank's work to solve the equation 25=x/4 −9
is shown below. In which step did Hank make a mistake, and what mistake did he make?
25=x/4 −9
Step 1: 16=x/4
Step 2: x=64
is shown below. In which step did Hank make a mistake, and what mistake did he make?
25=x/4 −9
Step 1: 16=x/4
Step 2: x=64
Answers
Answer
and from these four answers 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 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.
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.
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what is the right one
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 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.
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.
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what is the right one
Answered by
GPT-4o mini
Hank made a mistake in Step 1 of his solution.
He started with the equation:
\[ 25 = \frac{x}{4} - 9 \]
To isolate \(\frac{x}{4}\), he should have added 9 to both sides:
\[ 25 + 9 = \frac{x}{4} \]
This simplifies to:
\[ 34 = \frac{x}{4} \]
However, Hank wrote:
\[ 16 = \frac{x}{4} \]
which is incorrect.
In Step 2, he correctly multiplied both sides by 4 to solve for \(x\):
\[ x = 64 \]
But because the previous step was incorrect, the value of \(x\) is also incorrect. The correct value after performing the correct operations from the beginning would be:
\[ x = 34 \cdot 4 = 136 \]
So, the mistake was in Step 1, where he incorrectly calculated \(25 + 9\) as 16 instead of 34.
He started with the equation:
\[ 25 = \frac{x}{4} - 9 \]
To isolate \(\frac{x}{4}\), he should have added 9 to both sides:
\[ 25 + 9 = \frac{x}{4} \]
This simplifies to:
\[ 34 = \frac{x}{4} \]
However, Hank wrote:
\[ 16 = \frac{x}{4} \]
which is incorrect.
In Step 2, he correctly multiplied both sides by 4 to solve for \(x\):
\[ x = 64 \]
But because the previous step was incorrect, the value of \(x\) is also incorrect. The correct value after performing the correct operations from the beginning would be:
\[ x = 34 \cdot 4 = 136 \]
So, the mistake was in Step 1, where he incorrectly calculated \(25 + 9\) as 16 instead of 34.
Answered by
GPT-4o mini
The correct statement regarding 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.**
In the original equation \( 25 = \frac{x}{4} - 9 \), Hank should have added 9 to both sides to isolate \(\frac{x}{4}\). Instead, he incorrectly led to \( 16 = \frac{x}{4} \). This choice accurately points out the nature of his mistake in Step 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.**
In the original equation \( 25 = \frac{x}{4} - 9 \), Hank should have added 9 to both sides to isolate \(\frac{x}{4}\). Instead, he incorrectly led to \( 16 = \frac{x}{4} \). This choice accurately points out the nature of his mistake in Step 1.