Let's analyze each step that Jake followed while solving the equation:
1. [tex]\(\frac{1}{3}x + 7 = 15\)[/tex]
This is the given equation.
2. [tex]\(\frac{1}{3}x + 7 - 7 = 15\)[/tex]
In this step, Jake is attempting to isolate the term involving [tex]\(x\)[/tex] by subtracting 7 from both sides of the equation. However, the correct result after subtracting 7 from both sides should be:
[tex]\(\frac{1}{3}x + 7 - 7 = 15 - 7 \\
\frac{1}{3}x = 8\)[/tex]
Instead, Jake incorrectly shows [tex]\(\frac{1}{3}x = 15\)[/tex], which is incorrect.
3. [tex]\(\frac{1}{3}x = 15\)[/tex]
This step carries forward the mistake from step 2.
4. [tex]\(3 \cdot \frac{1}{3}x = 3 \cdot 15\)[/tex]
Multiplying both sides by 3 to solve for [tex]\(x\)[/tex]. Based on the incorrect premise from step 3, this step simplifies to [tex]\(x = 45\)[/tex], which is consistent with the incorrect calculation.
5. [tex]\(x = 45\)[/tex]
This is the final answer based on the incorrect steps.
Since the error occurred in step 2 where Jake's transformation was incorrect (it should have been [tex]\(\frac{1}{3}x = 8\)[/tex]), the correct answer is:
A. Jake made a mistake in step 2.
