Sehyr solved the equation w/2−7=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

w22=18/2
Using the Division Property of Equality

w=9


(1 point)

Answer 1

Let's analyze Sehyr's work step by step to identify her error and find the correct solution to the equation \( \frac{w}{2} - 7 = 11 \).

1. Starting Equation: \[ \frac{w}{2} - 7 = 11 \]

2. Applying the Addition Property of Equality: Sehyr correctly added 7 to both sides: \[ \frac{w}{2} - 7 + 7 = 11 + 7 \] Which simplifies correctly to: \[ \frac{w}{2} = 18 \]

3. Now, here is where Sehyr made a mistake in her next step: Sehyr wrote: \[ \frac{w}{2} = \frac{18}{2} \] This is incorrect. She incorrectly wrote \(\frac{w}{2} = \frac{18}{2}\) instead of simply dividing 18 by the correct number which is 2.

4. Correct step: To isolate \(w\), you should multiply both sides by 2: \[ w = 18 \cdot 2 \]

5. Final Solution: \[ w = 36 \]

Thus, the correct solution to the equation \( \frac{w}{2} - 7 = 11 \) is: \[ \boxed{36} \]