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 go through Sehyr's work step by step to identify the error and find the correct solution.

1. Starting with the original equation: \[ \frac{w}{2} - 7 = 11 \]

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

3. Sehyr then seems to have made an error in the next step. She wrote: \[ \frac{w}{2}/2 = \frac{18}{2} \] This step is incorrect because it’s not a proper application of the Division Property of Equality. The correct operation should be to multiply both sides by 2 to isolate \( w \).

4. Multiplying both sides by 2: \[ 2 \cdot \frac{w}{2} = 2 \cdot 18 \] This simplifies to: \[ w = 36 \]

Thus, the correct solution to the equation is: \[ \text{The solution to the equation is } 36. \]