2. solve \$|x| = -7\$. \$\\{-7, 7\\}\$ \$\\{-7\\}\$ \$\\{7\\}\$ no solutions

2. solve \$|x| = -7\$. \$\\{-7, 7\\}\$ \$\\{-7\\}\$ \$\\{7\\}\$…

QUESTION IMAGE

$2. solve \$|x| = -7\$. \$\\{-7, 7\\}\$ \$\\{-7\\}\$ \$\\{7\\}\$…$

Question

solve \$|x| = -7\$.

\$\\{-7, 7\\}\$

\$\\{-7\\}\$

\$\\{7\\}\$

no solutions

Explanation:

Response

<pre_analysis>
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"needs_drawing": false,
"concepts_used": [
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"new_concepts": [],
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</pre_analysis>

Analyze the absolute value equation

Using the Absolute Value Equations knowledge point
\[
|x| = -7
\]

Determine the number of solutions

Using the Number of Solutions of Absolute Value Equations knowledge point
\[

\begin{aligned} &\text{Since } |x| \ge 0 \text{ for all real numbers } x,\\ &\text{the equation } |x| = -7 \text{ has no real solutions.} \end{aligned}

\]
</reasoning>

<answer>
<mcq-option>(A) $\{-7, 7\}$</mcq-option>
<mcq-option>(B) $\{-7\}$</mcq-option>
<mcq-option>(C) $\{7\}$</mcq-option>
<mcq-correct>(D) no solutions</mcq-correct>
</answer>

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

Answer: