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solve each equation: \\(\\frac{1}{3} = \\frac{x}{18}\\) answer example:…

Question

solve each equation:

\\(\frac{1}{3} = \frac{x}{18}\\)

answer
example: x=3; x=5

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Cross Product Property",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Set up the proportion equation

\[
\frac{1}{3} = \frac{x}{18}
\]

Apply cross-multiplication

\[
3 \cdot x = 1 \cdot 18
\]

Solve for x

\[

$$\begin{aligned} 3x &= 18 \\ x &= 6 \end{aligned}$$

\]
</reasoning>

<answer>
Solve each equation:

\(\frac{1}{3} = \frac{x}{18}\)

\(x =\) <blank>\(6\)</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Cross Product Property",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Set up the proportion equation

\[
\frac{1}{3} = \frac{x}{18}
\]

Apply cross-multiplication

\[
3 \cdot x = 1 \cdot 18
\]

Solve for x

\[

$$\begin{aligned} 3x &= 18 \\ x &= 6 \end{aligned}$$

\]
</reasoning>

<answer>
Solve each equation:

\(\frac{1}{3} = \frac{x}{18}\)

\(x =\) <blank>\(6\)</blank>
</answer>

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