Question

Ms. Wilson is solving the equation 23x−7=5 for x. Her steps are as follows: 23x−7=5 Step 1: 23x−7+7=5+7 Step 2: 23x=12 Step 3: (23)(23x)=12(23) Step 4: x=8 Ms. Wilson made a mistake in Response area. The correct answer to this problem is Response area. x=36Step 1Step 2x=12No mistakes were made.x=18Step 3Step 4x=−18

Answer 1

Let's go through Ms. Wilson's steps one by one to find the correct solution to the equation \( 23x - 7 = 5 \).

1. **Starting equation**:
\[
23x - 7 = 5
\]

2. **Step 1**: Add 7 to both sides:
\[
23x - 7 + 7 = 5 + 7
\]
This simplifies to:
\[
23x = 12
\]

3. **Step 2**: Now that we have \( 23x = 12 \), Ms. Wilson tries to simplify this further. However, her next steps seem incorrect because she incorrectly multiplied both sides by 23.

**To find x**, we should divide both sides by 23:
\[
x = \frac{12}{23}
\]

4. **Conclusion**: The solution is:
\[
x = \frac{12}{23}
\]

Given the options you provided:
- \( x = 36 \)
- \( x = 12 \)
- No mistakes were made.
- \( x = 18 \)
- \( x = -18 \)

It appears Ms. Wilson made a mistake in Step 3 when she multiplied both sides incorrectly. The correct solution is \( \frac{12}{23} \), which does not match any of the given answer choices. Therefore, the most accurate assessment is that **mistakes were made** in solving the equation.

If you'd like to express the final answer in a different context, please let me know!