Sehyr solved the equation w2−7=11

Question

. 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:

w2−7=11


w2−7+7=11+7
Using the Addition Property of Equality

w22=182
Using the Division Property of Equality

w=9


(1 point)
The solution to the equation is
.

Answer 1

Let's analyze Sehyr's work step by step to identify the error and find the correct solution to the equation \( w^2 - 7 = 11 \).

1. Starting Equation: \[ w^2 - 7 = 11 \]

2. Applying the Addition Property of Equality: Sehyr correctly added 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]

3. Error in the Division Property of Equality: Sehyr incorrectly wrote: \[ w^2 / 2 = 18 / 2 \] This is incorrect because it implies she divided both sides by 2 when she shouldn't have, as there is no need to divide by 2 at this step.

4. Correct Step: Instead of dividing, we should find \( w \) by taking the square root of both sides: \[ w = \sqrt{18} \quad \text{or} \quad w = -\sqrt{18} \]

5. Further Simplifying: \[ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \] So the complete solutions are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]

Thus, the corrected solutions to the equation \( w^2 - 7 = 11 \) are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]

Answer 2

um how would that be shown? i cant read you asnwer with the whole 'text' and 'quad'

Answer 3

I apologize for the confusion. Here's the solution written out more clearly without the extra formatting:

1. Start with the original equation: \( w^2 - 7 = 11 \)

2. Add 7 to both sides: \( w^2 - 7 + 7 = 11 + 7 \)
   This simplifies to:
   \( w^2 = 18 \)

3. Take the square root of both sides: \( w = \sqrt{18} \) or \( w = -\sqrt{18} \)

4. Simplify the square root: \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \) So we have:
   \( w = 3\sqrt{2} \) or \( w = -3\sqrt{2} \)

Thus, the solutions to the equation are:

• \( w = 3\sqrt{2} \)
• \( w = -3\sqrt{2} \)

If you need numerical approximations:

• \( w \approx 4.24 \) (for \( 3\sqrt{2} \))
• \( w \approx -4.24 \) (for \( -3\sqrt{2} \))

I hope this format is easier to read!

Answer 4

- \( w = -3\sqrt{2} \)

Answer 5

Yes, that's correct! The solutions to the equation \( w^2 - 7 = 11 \) are:

1. \( w = 3\sqrt{2} \)
2. \( w = -3\sqrt{2} \)

If you need further clarification:

• Positive solution: \( w = 3\sqrt{2} \) is approximately \( 4.24 \).
• Negative solution: \( w = -3\sqrt{2} \) is approximately \( -4.24 \).

Both solutions are valid and represent the values of \( w \) that satisfy the original equation.

If you have any more questions or need help with another concept, feel free to ask!