Let's analyze the given statement and the properties available:
1. Statement: If [tex]\(9x = 27\)[/tex], then [tex]\(27 = 9x\)[/tex].
2. Explanation:
- Symmetric Property: The symmetric property of equality states that if [tex]\(a = b\)[/tex], then [tex]\(b = a\)[/tex]. This property justifies swapping the left-hand side and the right-hand side of an equality.
Step-by-Step Analysis:
1. Equation Given: [tex]\(9x = 27\)[/tex].
2. According to the symmetric property of equality, if [tex]\(a = b\)[/tex], then [tex]\(b = a\)[/tex].
3. Applying this property here:
- Consider [tex]\(a\)[/tex] as [tex]\(9x\)[/tex] and [tex]\(b\)[/tex] as [tex]\(27\)[/tex].
- If [tex]\(9x = 27\)[/tex] (which is true as per the given equation),
- Then by the symmetric property, [tex]\(27 = 9x\)[/tex].
Therefore, the property that justifies the statement "if [tex]\(9x = 27\)[/tex], then [tex]\(27 = 9x\)[/tex]" is the symmetric property.
Answer: C. Symmetric Property
