Question

evaluate the following.

\\\left| |-15| - |6 - 12| \
ight|\\

Explanation:

<pre_analysis>
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</pre_analysis>

<reasoning>

Evaluate the inner terms

We first evaluate the inner absolute value expressions.
\[
|-15| = 15
\]
\[

6 - 12

=

-6

= 6

\]

Substitute and simplify

We substitute these values back into the main expression.
\[
\Big| |-15| - |6 - 12| \Big| = |15 - 6|
\]

Calculate the final absolute value

We perform the subtraction and apply the outer absolute value.
\[

15 - 6

=

9

= 9

\]
</reasoning>

<answer>
Evaluate the following.
\[ \Big| |-15| - |6 - 12| \Big| = \] <blank>9</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Absolute Value",
"Order of Operations"
],
"current_concepts": [
"Absolute Value",
"Order of Operations",
"Integer Arithmetic"
]
}
</pre_analysis>

<reasoning>

Evaluate the inner terms

We first evaluate the inner absolute value expressions.
\[
|-15| = 15
\]
\[

6 - 12

=

-6

= 6

\]

Substitute and simplify

We substitute these values back into the main expression.
\[
\Big| |-15| - |6 - 12| \Big| = |15 - 6|
\]

Calculate the final absolute value

We perform the subtraction and apply the outer absolute value.
\[

15 - 6

=

9

= 9

\]
</reasoning>

<answer>
Evaluate the following.
\[ \Big| |-15| - |6 - 12| \Big| = \] <blank>9</blank>
</answer>

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