Question

solve by first clearing decimals.

\\-3.2 = -4 + 0.8b\\

Explanation:

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

<reasoning>

Multiply both sides by 10 to clear decimals

\[
10 \cdot (-3.2) = 10 \cdot (-4 + 0.8b)
\]
\[
-32 = -40 + 8b
\]

Isolate the variable term

\[
-32 + 40 = 8b
\]
\[
8 = 8b
\]

Solve for b

\[
b = \frac{8}{8}
\]
\[
b = 1
\]
</reasoning>

<answer>
\(b = 1\)
</answer>

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

Answer:

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

<reasoning>

Multiply both sides by 10 to clear decimals

\[
10 \cdot (-3.2) = 10 \cdot (-4 + 0.8b)
\]
\[
-32 = -40 + 8b
\]

Isolate the variable term

\[
-32 + 40 = 8b
\]
\[
8 = 8b
\]

Solve for b

\[
b = \frac{8}{8}
\]
\[
b = 1
\]
</reasoning>

<answer>
\(b = 1\)
</answer>

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