Question

Ms. Wilson is solving the equation ⅔x - 7 = 5 for x. Her steps are as follows:
⅔x - 7= 6
Stop 1: ⅔x - 7 + 7 = 5 + 7
Step 2: ⅔x = 12
Step 3: (⅔) (⅔x) = 12 (⅔)
Step 4: x = 8
Ms. Wilson made a mistake in _. The correct answer to this
problem is _.

Answer 1

Ms. Wilson made a mistake in **Stop 1**. She incorrectly wrote the equation as \( \frac{2}{3}x - 7 = 6 \) instead of \( \frac{2}{3}x - 7 = 5 \).

Let's solve the equation correctly:

Starting with the original equation:
\[
\frac{2}{3}x - 7 = 5
\]

**Step 1:** Add 7 to both sides:
\[
\frac{2}{3}x - 7 + 7 = 5 + 7
\]
\[
\frac{2}{3}x = 12
\]

**Step 2:** To isolate x, multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[
x = 12 \cdot \frac{3}{2}
\]
\[
x = 12 \cdot 1.5 = 18
\]

Thus, the correct answer to the problem is **18**.

To summarize:
Ms. Wilson made a mistake in **Stop 1**. The correct answer to this problem is **18**.