Question
Sehyr solved the equation w2−7=11
. She seems to have made an error in her work because the solution she found does not work. Observe Sehyr’s work to find her error and correct it to find the solution to the equation.
Sehyr’s work:
w/2−7=11
w/2−7+7=11+7
Using the Addition Property of Equality
w/2/2=18/2
Using the Division Property of Equality
w=9
(1 point)
The solution to the equation is
./
. She seems to have made an error in her work because the solution she found does not work. Observe Sehyr’s work to find her error and correct it to find the solution to the equation.
Sehyr’s work:
w/2−7=11
w/2−7+7=11+7
Using the Addition Property of Equality
w/2/2=18/2
Using the Division Property of Equality
w=9
(1 point)
The solution to the equation is
./
Answers
Answer
write it without words
Answer
what does sqrt stand for
Answer
so the answer is -3/2
Answered by
GPT-4o mini
Let's analyze Sehyr's work step by step to find the error.
1. She started with the equation:
\( w^2 - 7 = 11 \)
2. It appears that Sehyr incorrectly rewrote the equation as:
\( \frac{w}{2} - 7 = 11 \)
This is not correct, as the original equation contains \( w^2 \) not \( \frac{w}{2} \).
3. Instead, we should start from the correct original equation:
\( w^2 - 7 = 11 \)
4. Now, let's add 7 to both sides to isolate the \( w^2 \) term:
\( w^2 - 7 + 7 = 11 + 7 \)
This simplifies to:
\( w^2 = 18 \)
5. Next, we take the square root of both sides. Remember to consider both the positive and negative roots:
\( w = \pm \sqrt{18} \)
\( w = \pm 3\sqrt{2} \) (since \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \))
Thus, the corrected solution to the equation \( w^2 - 7 = 11 \) is:
**\( w = 3\sqrt{2} \) and \( w = -3\sqrt{2} \)**.
1. She started with the equation:
\( w^2 - 7 = 11 \)
2. It appears that Sehyr incorrectly rewrote the equation as:
\( \frac{w}{2} - 7 = 11 \)
This is not correct, as the original equation contains \( w^2 \) not \( \frac{w}{2} \).
3. Instead, we should start from the correct original equation:
\( w^2 - 7 = 11 \)
4. Now, let's add 7 to both sides to isolate the \( w^2 \) term:
\( w^2 - 7 + 7 = 11 + 7 \)
This simplifies to:
\( w^2 = 18 \)
5. Next, we take the square root of both sides. Remember to consider both the positive and negative roots:
\( w = \pm \sqrt{18} \)
\( w = \pm 3\sqrt{2} \) (since \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \))
Thus, the corrected solution to the equation \( w^2 - 7 = 11 \) is:
**\( w = 3\sqrt{2} \) and \( w = -3\sqrt{2} \)**.
Answered by
GPT-4o mini
Given:
\( w^2 - 7 = 11 \)
Step 1:
\( w^2 = 11 + 7 \)
Step 2:
\( w^2 = 18 \)
Step 3:
\( w = \pm \sqrt{18} \)
Step 4:
\( w = \pm 3\sqrt{2} \)
**Solution:**
\( w = 3\sqrt{2}, \; w = -3\sqrt{2} \)
\( w^2 - 7 = 11 \)
Step 1:
\( w^2 = 11 + 7 \)
Step 2:
\( w^2 = 18 \)
Step 3:
\( w = \pm \sqrt{18} \)
Step 4:
\( w = \pm 3\sqrt{2} \)
**Solution:**
\( w = 3\sqrt{2}, \; w = -3\sqrt{2} \)
Answered by
GPT-4o mini
The symbol \( \sqrt{} \) stands for "square root." It is a mathematical operation that finds a value which, when multiplied by itself, gives the original number. For example, \( \sqrt{4} = 2 \) because \( 2 \times 2 = 4 \). Similarly, \( \sqrt{9} = 3 \) because \( 3 \times 3 = 9 \). In general, the square root of a number \( x \) is a value \( y \) such that \( y^2 = x \).
Answered by
GPT-4o mini
The answer you're referring to, \(-\frac{3}{2}\), is not correct for the original equation \(w^2 - 7 = 11\).
To clarify:
1. Starting with the equation:
\( w^2 - 7 = 11 \)
2. Add 7 to both sides:
\( w^2 = 18 \)
3. Taking the square root of both sides gives:
\( w = \pm \sqrt{18} \)
This simplifies to:
\( w = \pm 3\sqrt{2} \)
Thus, the correct solutions to the equation are:
**\( w = 3\sqrt{2} \) and \( w = -3\sqrt{2} \)**.
If you intended to solve a different equation or if there's any confusion, please let me know!
To clarify:
1. Starting with the equation:
\( w^2 - 7 = 11 \)
2. Add 7 to both sides:
\( w^2 = 18 \)
3. Taking the square root of both sides gives:
\( w = \pm \sqrt{18} \)
This simplifies to:
\( w = \pm 3\sqrt{2} \)
Thus, the correct solutions to the equation are:
**\( w = 3\sqrt{2} \) and \( w = -3\sqrt{2} \)**.
If you intended to solve a different equation or if there's any confusion, please let me know!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.