Question

Ms. Turner is solving the equation 16 = -2 (k + 9). Her steps are shown below. In what step, if any, did Ms. Turner make a mistake?

16 = -2 (k + 9)

Step 1: 16 = -2k - 18
Step 2: 16 + 18 = -2k - 18 + 18
Step 3: 34 = -2k
Step 4: 34/-2 = -2k/-2
Step 5: k = -17

- Step 1
- Step 2
- Step 3
- Step 4
- Step 5
- Ms. Turner did not make a mistake.

Answer 1

Let's go through Ms. Turner's steps to check for any mistakes:

1. **Step 1**: Ms. Turner rewrites the equation from the original:
\[
16 = -2(k + 9) \implies 16 = -2k - 18
\]
This step is **correct**.

2. **Step 2**: She adds 18 to both sides:
\[
16 + 18 = -2k - 18 + 18 \implies 34 = -2k
\]
This step is **also correct**.

3. **Step 3**: She correctly shows:
\[
34 = -2k
\]
This step is **correct**.

4. **Step 4**: Ms. Turner divides both sides by -2:
\[
\frac{34}{-2} = \frac{-2k}{-2} \implies -17 = k
\]
This step is **correct**.

5. **Step 5**: She states that \( k = -17 \).

Upon examining all of the steps, Ms. Turner did **not** make any mistakes. The final answer she provided, \( k = -17 \), is indeed correct.

Thus, the conclusion is:

- **Ms. Turner did not make a mistake.**