Question

jake solved an equation, as shown.

\

$$\begin{array}{|c|c|} \\hline \\textbf{step} & \\textbf{statement} \\\\ \\hline 1 & \\frac{1}{3}x + 7 = 15 \\\\ \\hline 2 & \\frac{1}{3}x + 7 - 7 = 15 \\\\ \\hline 3 & \\frac{1}{3}x = 15 \\\\ \\hline 4 & 3 \\cdot \\frac{1}{3}x = 3 \\cdot 15 \\\\ \\hline 5 & x = 45 \\\\ \\hline \\end{array}$$

which statement is true?

• jake made a mistake in step 2.
• jake made a mistake in step 4.
• jake made a mistake in step 5.
• jake solved the equation correctly.

Explanation:

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<reasoning>

Analyze the given equation and Step 1

The original equation Jake is solving in Step 1 is:
\[\frac{1}{3}x + 7 = 15\]

Evaluate Step 2

In Step 2, Jake attempts to subtract \(7\) from both sides of the equation to isolate the variable term.
Using the Properties of Equality, if you subtract a number from one side of an equation, you must subtract the same number from the other side to keep the equation balanced:
\[\frac{1}{3}x + 7 - 7 = 15 - 7\]
However, Jake's Step 2 statement is:
\[\frac{1}{3}x + 7 - 7 = 15\]
Jake subtracted \(7\) only from the left side and failed to subtract \(7\) from the right side. This is an algebraic error.

Evaluate Step 3

In Step 3, Jake simplifies his incorrect Step 2 expression:
\[\frac{1}{3}x = 15\]
While the left side simplifies correctly (\(7 - 7 = 0\)), the equation is already incorrect because the right side should have been \(15 - 7 = 8\). Thus, the mistake was initiated in Step 2.

Identify the correct statement

Since Jake failed to apply the subtraction property of equality properly in Step 2, the true statement is that Jake made a mistake in Step 2.
</reasoning>

<answer>
<mcq-correct>Jake made a mistake in step 2.</mcq-correct>
<mcq-option>Jake made a mistake in step 4.</mcq-option>
<mcq-option>Jake made a mistake in step 5.</mcq-option>
<mcq-option>Jake solved the equation correctly.</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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Answer:

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<reasoning>

Analyze the given equation and Step 1

The original equation Jake is solving in Step 1 is:
\[\frac{1}{3}x + 7 = 15\]

Evaluate Step 2

In Step 2, Jake attempts to subtract \(7\) from both sides of the equation to isolate the variable term.
Using the Properties of Equality, if you subtract a number from one side of an equation, you must subtract the same number from the other side to keep the equation balanced:
\[\frac{1}{3}x + 7 - 7 = 15 - 7\]
However, Jake's Step 2 statement is:
\[\frac{1}{3}x + 7 - 7 = 15\]
Jake subtracted \(7\) only from the left side and failed to subtract \(7\) from the right side. This is an algebraic error.

Evaluate Step 3

In Step 3, Jake simplifies his incorrect Step 2 expression:
\[\frac{1}{3}x = 15\]
While the left side simplifies correctly (\(7 - 7 = 0\)), the equation is already incorrect because the right side should have been \(15 - 7 = 8\). Thus, the mistake was initiated in Step 2.

Identify the correct statement

Since Jake failed to apply the subtraction property of equality properly in Step 2, the true statement is that Jake made a mistake in Step 2.
</reasoning>

<answer>
<mcq-correct>Jake made a mistake in step 2.</mcq-correct>
<mcq-option>Jake made a mistake in step 4.</mcq-option>
<mcq-option>Jake made a mistake in step 5.</mcq-option>
<mcq-option>Jake solved the equation correctly.</mcq-option>
</answer>

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