Question

solve by first clearing decimals.

\\4.6 = 4 - 0.075p\\

Explanation:

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"new_concepts": [
"Clearing Decimals",
"Linear Equations"
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"current_concepts": [
"Clearing Decimals",
"Linear Equations",
"Decimal Arithmetic"
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</pre_analysis>

<reasoning>

Multiply by a power of ten to clear decimals

\[

$$\begin{aligned} 1000 \cdot (4.6) &= 1000 \cdot (4 - 0.075p) \\ 4600 &= 4000 - 75p \end{aligned}$$

\]

Isolate the variable term

\[

$$\begin{aligned} 4600 - 4000 &= -75p \\ 600 &= -75p \end{aligned}$$

\]

Solve for p

\[

$$\begin{aligned} p &= \frac{600}{-75} \\ p &= -8 \end{aligned}$$

\]
</reasoning>

<answer>
\(p = -8\)
</answer>

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

Answer:

<pre_analysis>
{
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"step_cot",
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],
"needs_drawing": false,
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],
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"Clearing Decimals",
"Linear Equations",
"Decimal Arithmetic"
]
}
</pre_analysis>

<reasoning>

Multiply by a power of ten to clear decimals

\[

$$\begin{aligned} 1000 \cdot (4.6) &= 1000 \cdot (4 - 0.075p) \\ 4600 &= 4000 - 75p \end{aligned}$$

\]

Isolate the variable term

\[

$$\begin{aligned} 4600 - 4000 &= -75p \\ 600 &= -75p \end{aligned}$$

\]

Solve for p

\[

$$\begin{aligned} p &= \frac{600}{-75} \\ p &= -8 \end{aligned}$$

\]
</reasoning>

<answer>
\(p = -8\)
</answer>

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