Question

Sehyr solved the equation w/2−7=11. 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.

w/2−7=11

w/2−7+7=11+7 Using the Addition Property of Equality

w/2/2=182 Using the Division Property of Equality

w=9

The solution to the equation is

Answer 1

Let's go through Sehyr's work step by step to identify and correct her error.

1. The original equation is:
\[
\frac{w}{2} - 7 = 11
\]

2. Sehyr then applies the Addition Property of Equality:
\[
\frac{w}{2} - 7 + 7 = 11 + 7
\]
This simplifies correctly to:
\[
\frac{w}{2} = 18
\]

3. Sehyr then incorrectly writes:
\[
\frac{w}{2}/2 = 182
\]
This is where the error occurs. To isolate \( w \), we need to multiply both sides of the equation by 2 (not divide).

Correctly applying this step, we have:
\[
\frac{w}{2} = 18
\]
Now multiply both sides by 2:
\[
w = 18 \cdot 2
\]

4. Simplifying gives:
\[
w = 36
\]

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