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

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 observe Sehyr’s work to identify the error and then solve the equation correctly.

Sehyr starts with the equation: \[ \frac{w}{2} - 7 = 11 \]

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

2. However, the next step is where she made the error. Sehyr wrote: \[ \frac{w}{2}/2 = \frac{18}{2} \] This notation is incorrect. The correct step is to multiply both sides by 2 to solve for \( w \).

So, we should be multiplying both sides by 2, not dividing: \[ 2 \cdot \frac{w}{2} = 2 \cdot 18 \] This simplifies to: \[ w = 36 \]

Thus, the correct solution to the equation is: \[ \boxed{36} \]