Final answer:
The property used in the expression [4 + (-2)] + 1 = 4 + [(-2) + 1] is the Associative Property of Addition, which allows the regrouping of addends without changing the sum, as demonstrated in the example (2 + 3) + 4 = 2 + (3 + 4).
Step-by-step explanation:
The property used to find the equivalent expression [4 + (-2)] + 1 = 4 + [(-2) + 1] is the Associative Property of Addition. This property states that when three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example, (a + b) + c = a + (b + c). In this case, the expression inside the parentheses is calculated first, and this can be changed without affecting the result of the sum.
To understand this, consider a more straightforward example: (2 + 3) + 4 = 2 + (3 + 4). Both sides result in 9, demonstrating how the grouping does not affect the final sum. Applying this to our initial problem, when we move the parenthesis from [4 + (-2)] to [(-2) + 1], we are using the Associative Property to regroup the numbers, which shows that the addition of numbers is associative regardless of their signs as well.