Let's analyze Sehyr's work step by step to identify her error and find the correct solution.
She started with the equation:
\[ w^2 - 7 = 11 \]
-
Adding 7 to both sides:
Sehyr correctly applied the Addition Property of Equality:\[ w^2 - 7 + 7 = 11 + 7 \]
Simplifying gives:
\[ w^2 = 18 \] -
Here is where the error occurs:
In her next step, Sehyr incorrectly wrote:\[ w^2 = 18 \]
but improperly wrote \( w^2/2 = 182 \), which is incorrect. The correct step should be to take the square root of both sides. -
Taking the square root:
The correct next step would be:\[ w = \pm \sqrt{18} \]
Simplifying \( \sqrt{18} \) gives:
\[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \] -
Final solutions:
Therefore, the solutions are:\[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]
So, Sehyr's error was in handling the equation after adding 7. The correct solutions to the equation \( w^2 - 7 = 11 \) are \( w = 3\sqrt{2} \) and \( w = -3\sqrt{2} \).