Question

match each equation with its solution.

equation
\\(\frac{n}{5} = -\frac{1}{5}\\)
\\(n + 15 = -10\\)
\\(-5n = 1\\)
\\(n - 13 = -12\\)

solution
\\(n = -\frac{1}{5}\\)
\\(n = -1\\)
\\(n = -25\\)
\\(n = 1\\)

Explanation:

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<reasoning>

Solve first equation

\[

$$\begin{aligned} \frac{n}{5} &= -\frac{1}{5} \\ n &= -1 \end{aligned}$$

\]

Solve second equation

\[

$$\begin{aligned} n + 15 &= -10 \\ n &= -25 \end{aligned}$$

\]

Solve third and fourth equations

\[

$$\begin{aligned} -5n &= 1 \implies n = -\frac{1}{5} \\ n - 13 &= -12 \implies n = 1 \end{aligned}$$

\]
</reasoning>

<answer>

Equation	Solution
\(n + 15 = -10\)	\(n = -25\)
\(-5n = 1\)	\(n = -\frac{1}{5}\)
\(n - 13 = -12\)	\(n = 1\)

</answer>

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

Answer:

<pre_analysis>
{
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"step_cot",
"table_formatter",
"explain_then_answer",
"quick"
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"concepts_used": [
"Solving Linear Equations"
],
"new_concepts": [],
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"Solving Linear Equations"
]
}
</pre_analysis>

<reasoning>

Solve first equation

\[

$$\begin{aligned} \frac{n}{5} &= -\frac{1}{5} \\ n &= -1 \end{aligned}$$

\]

Solve second equation

\[

$$\begin{aligned} n + 15 &= -10 \\ n &= -25 \end{aligned}$$

\]

Solve third and fourth equations

\[

$$\begin{aligned} -5n &= 1 \implies n = -\frac{1}{5} \\ n - 13 &= -12 \implies n = 1 \end{aligned}$$

\]
</reasoning>

<answer>

Equation	Solution
\(n + 15 = -10\)	\(n = -25\)
\(-5n = 1\)	\(n = -\frac{1}{5}\)
\(n - 13 = -12\)	\(n = 1\)

</answer>

<post_analysis>
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"Mathematics",
"Algebra",
"Solving Linear Equations"
]
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