Identify the properties

( 5 + 3) + 4 = ( 3 + 5) + 4 = Communitive property

( 3 × 2) × 8 = 3 × ( 2 × 8) = associative property

No, both of these are wrong.

The first is associative, the second is communicative.

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x+3y=-6

3x+9y=6

To identify the properties used in the given equations, we can start by understanding the properties themselves.

1. Commutative Property: This property states that the order in which two numbers are added or multiplied does not affect the result. In other words, you can switch the order of the numbers without changing the outcome.

2. Associative Property: This property applies to addition and multiplication and states that the grouping of numbers being added or multiplied does not affect the result. In other words, you can regroup the numbers without changing the outcome.

Now, let's analyze the equations provided:

Equation 1: (5 + 3) + 4 = (3 + 5) + 4

To check if the commutative property is being used, we can see if the order of the numbers is changed.

Here, we can observe that the order of the numbers being added does not change. Both sides of the equation have the same set of numbers, just in a different order. Therefore, the commutative property is being used.

Equation 2: (3 × 2) × 8 = 3 × (2 × 8)

To check if the associative property is being used, we can see if the grouping of the numbers being multiplied changes.

Here, we can observe that the numbers are rearranged, but no numbers are added or subtracted. The grouping of the numbers being multiplied is changed from left-to-right to right-to-left, but the overall multiplication operation and the result remain the same. Thus, the associative property is being used.

In summary:
- The commutative property is being used in Equation 1.
- The associative property is being used in Equation 2.