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solve for a. \\\\frac{a}{3} + 5 = 1\\ \\a = ?\\

Question

solve for a.

\\\frac{a}{3} + 5 = 1\\

\\a = ?\\

Explanation:

Response

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"skills_matched": [
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"needs_drawing": false,
"concepts_used": [
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<reasoning>

Isolate the variable term

Using the Linear Equations knowledge point
\[

$$\begin{aligned} \frac{a}{3} + 5 &= 1 \\ \frac{a}{3} &= 1 - 5 \\ \frac{a}{3} &= -4 \end{aligned}$$

\]

Solve for a

Using the Linear Equations knowledge point
\[

$$\begin{aligned} a &= -4 \cdot 3 \\ a &= -12 \end{aligned}$$

\]
</reasoning>

<answer>
Solve for a.
\[\frac{a}{3} + 5 = 1\]
\(a =\) <blank>-12</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Linear Equations",
"Algebraic Simplification"
]
}
</pre_analysis>

<reasoning>

Isolate the variable term

Using the Linear Equations knowledge point
\[

$$\begin{aligned} \frac{a}{3} + 5 &= 1 \\ \frac{a}{3} &= 1 - 5 \\ \frac{a}{3} &= -4 \end{aligned}$$

\]

Solve for a

Using the Linear Equations knowledge point
\[

$$\begin{aligned} a &= -4 \cdot 3 \\ a &= -12 \end{aligned}$$

\]
</reasoning>

<answer>
Solve for a.
\[\frac{a}{3} + 5 = 1\]
\(a =\) <blank>-12</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
</post_analysis>