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)

Answer 1

Let's go through Sehyr’s work step by step and identify the error.

1. Starting with the equation: \[ w^2 - 7 = 11 \]

2. She correctly added 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]

3. However, Sehyr then incorrectly used the Division Property of Equality. She wrote: \[ w^2 = 18 \implies w^2/2 = 18/2 \] and ended up with: \[ w^2 = 9 \]

   The last step "w²/2 = 18/2" was incorrect. Instead, we should take the square root of both sides of the equation \( w^2 = 18 \).

4. Correcting from \( w^2 = 18 \): \[ w = \pm \sqrt{18} \] This can be simplified: \[ w = \pm \sqrt{9 \cdot 2} = \pm 3\sqrt{2} \]

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