Let's solve the equation step by step to identify any potential errors Sehyr might have made.
The equation given is:
\[ \frac{w}{2} - 7 = 11 \]
To isolate \( w \), we'll first add 7 to both sides of the equation:
\[ \frac{w}{2} = 11 + 7 \]
This simplifies to:
\[ \frac{w}{2} = 18 \]
Next, we multiply both sides by 2 to eliminate the fraction:
\[ w = 18 \times 2 \]
This gives us:
\[ w = 36 \]
Now, let's verify the solution by substituting \( w = 36 \) back into the original equation:
\[ \frac{36}{2} - 7 = 11 \]
Calculating that, we get:
\[ 18 - 7 = 11 \]
Since this is true, \( w = 36 \) is indeed the correct solution.
If Sehyr's solution does not match this, her error could have occurred during any of the steps. Common mistakes could include incorrectly adding or multiplying, or misinterpreting the equation.
A specific example of a mistake could be if she did not correctly add 7 to the right side when trying to isolate \(\frac{w}{2}\), which would lead to a wrong equation. If she ended up with:
\[ \frac{w}{2} = 4 \quad \text{(for example, failing to properly calculate 11 + 7)} \]
And then multiplied incorrectly, it would lead her to a different value for \( w \).
In summary, if Sehyr arrived at a solution different from 36, she likely made an arithmetic error while manipulating the equation.