Question

solve for (x).

(6(x+5) = -7(2x-6) + 5x)

simplify your answer as much as possible.

(x = )

Explanation:

<pre_analysis>
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<reasoning>

Apply the distributive property

\[

$$\begin{aligned} 6(x+5) &= 6x + 30 \\ -7(2x-6) + 5x &= -14x + 42 + 5x \end{aligned}$$

\]

Combine like terms

\[

$$\begin{aligned} 6x + 30 &= (-14x + 5x) + 42 \\ 6x + 30 &= -9x + 42 \end{aligned}$$

\]

Solve for x

\[

$$\begin{aligned} 6x + 9x &= 42 - 30 \\ 15x &= 12 \\ x &= \frac{12}{15} \\ x &= \frac{4}{5} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(x\).

\(6(x+5)=-7(2x-6)+5x\)

Simplify your answer as much as possible.

\(x =\) <blank>\(\frac{4}{5}\)</blank>
</answer>

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

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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],
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"Distributive Property",
"Linear Equation Solutions"
],
"new_concepts": [],
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</pre_analysis>

<reasoning>

Apply the distributive property

\[

$$\begin{aligned} 6(x+5) &= 6x + 30 \\ -7(2x-6) + 5x &= -14x + 42 + 5x \end{aligned}$$

\]

Combine like terms

\[

$$\begin{aligned} 6x + 30 &= (-14x + 5x) + 42 \\ 6x + 30 &= -9x + 42 \end{aligned}$$

\]

Solve for x

\[

$$\begin{aligned} 6x + 9x &= 42 - 30 \\ 15x &= 12 \\ x &= \frac{12}{15} \\ x &= \frac{4}{5} \end{aligned}$$

\]
</reasoning>

<answer>
Solve for \(x\).

\(6(x+5)=-7(2x-6)+5x\)

Simplify your answer as much as possible.

\(x =\) <blank>\(\frac{4}{5}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equation Solutions"
]
}
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