Let's first review Sehyr's work and identify where the error occurred.
Sehyr started with the equation: \[ w^2 - 7 = 11 \]
She added 7 to both sides correctly: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]
The error occurs in the next step:
Sehyr wrote: \[ w^2 \div 2 = 18 \div 2 \] This is not correct. The correct step is to take the square root of both sides.
So instead of dividing by 2, we take the square root: \[ w = \pm \sqrt{18} \]
Now, we can simplify \(\sqrt{18}\): \[ w = \pm \sqrt{9 \cdot 2} = \pm \sqrt{9} \cdot \sqrt{2} = \pm 3\sqrt{2} \]
Thus, the solution to the equation is: \[ w = 3\sqrt{2} \quad \text{or} \quad w = -3\sqrt{2} \]
Final answer: \[ \text{The solution to the equation is } w = 3\sqrt{2} \text{ and } w = -3\sqrt{2}. \]