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 identify her error:

1. Original Equation: \( w^2 - 7 = 11 \)

2. Sehyr's First Step: She incorrectly rewrote the equation as: \[ \frac{w}{2} - 7 = 11 \] This is the first error. The original equation was \( w^2 - 7 = 11\), not \( \frac{w}{2} - 7 = 11 \).

3. Next Step: Sehyr tried to apply the Addition Property of Equality correctly by adding 7 to both sides: \[ \frac{w}{2} - 7 + 7 = 11 + 7 \ \Rightarrow \frac{w}{2} = 18 \]

4. Next Step: Then, she incorrectly used the Division Property of Equality: \[ \frac{w}{2}/2 = 18/2 \] Instead of this, she should simply multiply both sides by 2 to eliminate the fraction: \[ w = 18 \times 2 \ w = 36 \]

Correcting Sehyr's Work

Now, let's solve the original equation \( w^2 - 7 = 11 \) properly.

1. Start from the original equation: \[ w^2 - 7 = 11 \]

2. Add 7 to both sides: \[ w^2 = 11 + 7 \ w^2 = 18 \]

3. Take the square root of both sides: \[ w = \sqrt{18} \quad \text{or} \quad w = -\sqrt{18} \]

4. Simplifying \(\sqrt{18}\): \[ w = 3\sqrt{2} \quad \text{or} \quad w = -3\sqrt{2} \]

Final Solution

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