To determine which expression illustrates the associative property of addition, let's examine each option closely:
1. [tex]\((3 + 19) - 12 = (3 + 12) - 19\)[/tex]
- LHS: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- RHS: [tex]\((3 + 12) - 19 = 15 - 19 = -4\)[/tex]
- Comparison: [tex]\(10 \neq -4\)[/tex]
This expression is not true.
2. [tex]\(3 + (19 - 12) = 3 + (19 + 12)\)[/tex]
- LHS: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- RHS: [tex]\(3 + (19 + 12) = 3 + 31 = 34\)[/tex]
- Comparison: [tex]\(10 \neq 34\)[/tex]
This expression is not true.
3. [tex]\((3 + 19) - 12 = 3 + (19 - 12)\)[/tex]
- LHS: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- RHS: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Comparison: [tex]\(10 = 10\)[/tex]
This expression is true and shows the associative property.
4. [tex]\(3 + (19 - 12) = 3 - (19 + 12)\)[/tex]
- LHS: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- RHS: [tex]\(3 - (19 + 12) = 3 - 31 = -28\)[/tex]
- Comparison: [tex]\(10 \neq -28\)[/tex]
This expression is not true.
After evaluating all options, the valid expression that illustrates the associative property of addition is:
[tex]\((3 + 19) - 12 = 3 + (19 - 12)\)[/tex]
So, the correct option is:
[tex]\(\boxed{3}\)[/tex]
