Sure! Let's analyze each equation and match it with the corresponding property.
1. [tex]\[ -3(x+4) = -3x - 12 \][/tex]
- This equation shows how a term is distributed over a sum inside the parentheses. Specifically, the term [tex]\(-3\)[/tex] is distributed to both [tex]\(x\)[/tex] and [tex]\(4\)[/tex], resulting in [tex]\(-3x\)[/tex] and [tex]\(-12\)[/tex]. This is a classic example of the Distributive Property.
2. [tex]\[ 2 + x + 10 = 2 + 10 + x \][/tex]
- Here, the order of the terms [tex]\(x\)[/tex] and [tex]\(10\)[/tex] on the right side of the equation has been rearranged compared to the left side. This doesn't change the sum, demonstrating that the sum remains the same regardless of the order of addition. This is an example of the Commutative Property of Addition.
3. [tex]\[ 2 + (10 + x) = (2 + 10) + x \][/tex]
- This equation demonstrates how addition operations are grouped. On the left side, [tex]\(10\)[/tex] and [tex]\(x\)[/tex] are grouped together within parentheses, while on the right side, [tex]\(2\)[/tex] and [tex]\(10\)[/tex] are grouped together within parentheses. It shows that the sum remains the same regardless of how the numbers are grouped, illustrating the Associative Property of Addition.
Therefore, matching the given equations with the corresponding properties, we get:
- [tex]\[-3(x+4) = -3x - 12\][/tex] corresponds to the Distributive Property.
- [tex]\[2 + x + 10 = 2 + 10 + x\][/tex] corresponds to the Commutative Property.
- [tex]\[2 + (10 + x) = (2 + 10) + x\][/tex] corresponds to the Associative Property.
So, the final matching is:
- Distributive Property: [tex]\[-3(x+4) = -3x - 12\][/tex]
- Commutative Property: [tex]\[2 + x + 10 = 2 + 10 + x\][/tex]
- Associative Property: [tex]\[2 + (10 + x) = (2 + 10) + x\][/tex]
