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find the solution of the following equation. (3.75x + 15 = 63.75) (x = …

Question

find the solution of the following equation.

(3.75x + 15 = 63.75)

(x = 4)
(x = 8)
(x = 13)
(x = 17)

Explanation:

Response

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

<reasoning>

Subtract 15 from both sides

\[

$$\begin{aligned} 3.75x + 15 - 15 &= 63.75 - 15 \\ 3.75x &= 48.75 \end{aligned}$$

\]

Divide both sides by 3.75

\[

$$\begin{aligned} x &= \frac{48.75}{3.75} \\ x &= 13 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = 4\)</mcq-option>
<mcq-option>\(x = 8\)</mcq-option>
<mcq-correct>\(x = 13\)</mcq-correct>
<mcq-option>\(x = 17\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
</post_analysis>

Answer:

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

<reasoning>

Subtract 15 from both sides

\[

$$\begin{aligned} 3.75x + 15 - 15 &= 63.75 - 15 \\ 3.75x &= 48.75 \end{aligned}$$

\]

Divide both sides by 3.75

\[

$$\begin{aligned} x &= \frac{48.75}{3.75} \\ x &= 13 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = 4\)</mcq-option>
<mcq-option>\(x = 8\)</mcq-option>
<mcq-correct>\(x = 13\)</mcq-correct>
<mcq-option>\(x = 17\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
</post_analysis>