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:

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
./

Answer 1

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

Answer 2

write it without words

Answer 3

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:
\( w = 3\sqrt{2}, ; w = -3\sqrt{2} \)

Answer 4

what does sqrt stand for

Answer 5

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 \( y^2 = x \).

Answer 6

so the answer is -3/2

Answer 7

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!