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 workObserve Sehyr's work to find her error and correct it to find the solution to the equation . Sehyr's work w/2 - 7 = 11 Using the Addition Property of Equality w/2 - 7 + 7 = 11 + 7; w/2/2 = 18/2 Using the Division Property of Equality w = 9

Answer 1

Let's analyze Sehyr's work step by step to find her error and then solve the equation correctly.

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

### Step 1: Use the Addition Property of Equality
Sehyr added 7 to both sides:
\[
\frac{w}{2} - 7 + 7 = 11 + 7
\]
This simplifies correctly to:
\[
\frac{w}{2} = 18
\]

### Step 2: Use the Multiplication Property of Equality
Now, Sehyr writes:
\[
\frac{w}{2}/2 = 18/2
\]
This statement is incorrect because it applies the division incorrectly. Instead, to isolate \( w \), she should multiply both sides of the equation by 2 (the opposite of dividing by 2).

So, starting from:
\[
\frac{w}{2} = 18
\]
we multiply both sides by 2:
\[
w = 18 \cdot 2
\]

### Step 3: Calculate the solution
Calculating the right side gives:
\[
w = 36
\]

### Conclusion
The correct solution to the equation is:
\[
\boxed{36}
\]

Sehyr's error was in her handling of the division in the step after using the Addition Property of Equality. She should have multiplied both sides by 2 instead.