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.

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 analyze Sehyr's work step by step to see where the error occurred.

Starting with the equation:

\[ w/2 - 7 = 11 \]

Sehyr correctly added 7 to both sides:

\[ w/2 - 7 + 7 = 11 + 7 \]

This simplifies to:

\[ w/2 = 18 \]

However, in the next step, Sehyr incorrectly applied the Division Property. The correct step is to multiply both sides by 2 rather than dividing.

So, instead of doing:

\[ w/2/2 = 18/2 \]

it should be:

\[ w/2 = 18 \]

Now, multiplying both sides by 2 to solve for \( w \):

\[ w = 18 \times 2 \]
\[ w = 36 \]

Thus, the correct solution to the equation is:

\[ \text{The solution to the equation is } 36. \]