Answered

Select the correct answer.

Jake solved an equation, as shown.

\begin{tabular}{|c|c|}
\hline Step & Statement \\
\hline 1 & [tex]$\frac{1}{3} x + 7 = 15$[/tex] \\
\hline 2 & [tex]$\frac{1}{3} x + 7 - 7 = 15 - 7$[/tex] \\
\hline 3 & [tex]$\frac{1}{3} x = 8$[/tex] \\
\hline 4 & [tex]$3 \cdot \frac{1}{3} x = 3 \cdot 8$[/tex] \\
\hline 5 & [tex]$x = 24$[/tex] \\
\hline
\end{tabular}

Which statement is true?

A. Jake made a mistake in step 2.
B. Jake made a mistake in step 4.
C. Jake made a mistake in step 5.
D. Jake solved the equation correctly.



Answer :

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.