Property Identification C26725

1. **State the problem:** Identify the property illustrated by each equation or statement using properties numbered #1-9. 2. **Recall common algebraic properties:** - #1: Multiplicative Property of Zero: $a \cdot 0 = 0$ - #2: Associative Property of Addition: $(a + b) + c = a + (b + c)$ - #3: Reflexive Property of Equality: $a = a$ - #4: Distributive Property: $a(b + c) = ab + ac$ - #5: Additive Inverse Property: $a + (-a) = 0$ - #6: Symmetric Property of Equality: If $a = b$, then $b = a$ - #7: Additive Identity Property: $a + 0 = a$ - #8: Transitive Property of Equality: If $a = b$ and $b = c$, then $a = c$ - #9: Multiplicative Identity Property: $a \cdot 1 = a$ 3. **Identify each property:** A. $ab^2 \cdot 0 = 0$ uses #1 Multiplicative Property of Zero. B. $(7 + 5) + 1 = 7 + (5 + 1)$ uses #2 Associative Property of Addition. C. $6 = 6$ uses #3 Reflexive Property of Equality. D. $7(x - 3) = 7x - 21$ uses #4 Distributive Property. E. $x + (-x) = 0$ uses #5 Additive Inverse Property. F. if $y = 3$, then $3 = y$ uses #6 Symmetric Property of Equality. G. $(a + b) + 0 = 0 + (a + b)$ shows both sides equal but more closely matches #7 Additive Identity Property (though written symmetrically). H. if $x = -1$, and $-1 = z$, then $x = z$ uses #8 Transitive Property of Equality. I. $4x \cdot 1 = 4x$ uses #9 Multiplicative Identity Property. 4. **Summary:** - A: #1 - B: #2 - C: #3 - D: #4 - E: #5 - F: #6 - G: #7 - H: #8 - I: #9 This completes the identification of each property.