Question

which property of equality was used to solve this equation?

\\(x - 5 = -14\\)

\\(x - 5 + 5 = -14 + 5\\)

\\(x = -9\\)

addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality

Explanation:

<pre_analysis>
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<reasoning>

Analyze the equation transformation

\[

$$\begin{aligned} &\text{Original equation: } x - 5 = -14 \\ &\text{Next step: } x - 5 + 5 = -14 + 5 \end{aligned}$$

\]

Identify the operation performed

\[
\text{The number } 5 \text{ is added to both sides of the equation.}
\]

Match with the property of equality

\[
\text{Adding the same number to both sides of an equation is the addition property of equality.}
\]
</reasoning>

<answer>
<mcq-correct>addition property of equality</mcq-correct>
<mcq-option>subtraction property of equality</mcq-option>
<mcq-option>multiplication property of equality</mcq-option>
<mcq-option>division property of equality</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Properties of Equality"
]
}
</post_analysis>

Answer:

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"step_cot",
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"new_concepts": [
"Properties of Equality"
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"Properties of Equality"
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}
</pre_analysis>

<reasoning>

Analyze the equation transformation

\[

$$\begin{aligned} &\text{Original equation: } x - 5 = -14 \\ &\text{Next step: } x - 5 + 5 = -14 + 5 \end{aligned}$$

\]

Identify the operation performed

\[
\text{The number } 5 \text{ is added to both sides of the equation.}
\]

Match with the property of equality

\[
\text{Adding the same number to both sides of an equation is the addition property of equality.}
\]
</reasoning>

<answer>
<mcq-correct>addition property of equality</mcq-correct>
<mcq-option>subtraction property of equality</mcq-option>
<mcq-option>multiplication property of equality</mcq-option>
<mcq-option>division property of equality</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Properties of Equality"
]
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