Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

b. \\(-8x + 4 = 20 - 4x\\)

Question

b. \\(-8x + 4 = 20 - 4x\\)

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Multi-Step Equations",
"Combining Like Terms",
"Division Property of Equality"
],
"new_concepts": [],
"current_concepts": [
"Multi-Step Equations",
"Combining Like Terms",
"Division Property of Equality"
]
}
</pre_analysis>

<reasoning>

Add 4x to both sides

\[
-8x + 4 + 4x = 20 - 4x + 4x
\]
\[
-4x + 4 = 20
\]

Subtract 4 from both sides

\[
-4x + 4 - 4 = 20 - 4
\]
\[
-4x = 16
\]

Divide both sides by -4

\[
\frac{-4x}{-4} = \frac{16}{-4}
\]
\[
x = -4
\]
</reasoning>

<answer>
\(x = -4\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Multi-Step Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Multi-Step Equations",
"Combining Like Terms",
"Division Property of Equality"
],
"new_concepts": [],
"current_concepts": [
"Multi-Step Equations",
"Combining Like Terms",
"Division Property of Equality"
]
}
</pre_analysis>

<reasoning>

Add 4x to both sides

\[
-8x + 4 + 4x = 20 - 4x + 4x
\]
\[
-4x + 4 = 20
\]

Subtract 4 from both sides

\[
-4x + 4 - 4 = 20 - 4
\]
\[
-4x = 16
\]

Divide both sides by -4

\[
\frac{-4x}{-4} = \frac{16}{-4}
\]
\[
x = -4
\]
</reasoning>

<answer>
\(x = -4\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Multi-Step Equations"
]
}
</post_analysis>