Question

find the value of \\(x\\) given the image below.

a \\(x = 7\\)
b \\(x = 3\\)
c \\(x = 5\\)
d \\(x = 6\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Geometric Segment Solving",
"Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Geometric Segment Solving",
"Linear Equations",
"Segment Addition Postulate"
]
}
</pre_analysis>

<reasoning>

Set up the segment addition equation

\[
GH + HF = GF
\]
\[
3x + 19 = 28
\]

Solve for x

\[
3x = 28 - 19
\]
\[
3x = 9
\]
\[
x = 3
\]
</reasoning>

<answer>
<mcq-option>(A) \(x = 7\)</mcq-option>
<mcq-correct>(B) \(x = 3\)</mcq-correct>
<mcq-option>(C) \(x = 5\)</mcq-option>
<mcq-option>(D) \(x = 6\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Segment Solving"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Geometric Segment Solving",
"Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Geometric Segment Solving",
"Linear Equations",
"Segment Addition Postulate"
]
}
</pre_analysis>

<reasoning>

Set up the segment addition equation

\[
GH + HF = GF
\]
\[
3x + 19 = 28
\]

Solve for x

\[
3x = 28 - 19
\]
\[
3x = 9
\]
\[
x = 3
\]
</reasoning>

<answer>
<mcq-option>(A) \(x = 7\)</mcq-option>
<mcq-correct>(B) \(x = 3\)</mcq-correct>
<mcq-option>(C) \(x = 5\)</mcq-option>
<mcq-option>(D) \(x = 6\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Segment Solving"
]
}
</post_analysis>