Final answer:
The equation (3x+7)+(2x+8)=3x+7+2x+8 uses the Associative Property of Addition, which confirms that the sum remains the same regardless of the grouping of terms.
Step-by-step explanation:
The mathematical property used in the equation (3x+7)+(2x+8)=3x+7+2x+8 is called the Associative Property of Addition. This property states that it doesn't matter how we group the numbers when we're adding; the result will be the same. The numbers and variables inside the parentheses can be written out in a string without changing their value as per the associative rule.
Let's look at the Associative Property with ordinary numbers as an example: 2 + 3 is the same as 3 + 2. Similarly, in the equation provided, the sum is preserved regardless of how the terms are grouped. This concept emphasizes that the rules of mathematics are universally valid and independent of factors such as culture or geography.