Identify the property that justifies step 1 when solving the given equation 6x+2x-2=30
The property that justifies step 1 in solving the given equation 6x + 2x - 2 = 30 is the Distributive Property.
The property that justifies step 1 when solving the given equation 6x + 2x - 2 = 30 is the Commutative Property of Addition. This property allows us to rearrange the terms in any order without changing the sum. In this case, the terms 6x and 2x are added together by rearranging them in ascending order, resulting in 2x + 6x - 2 = 30.
To begin solving the given equation 6x + 2x - 2 = 30, let's focus on step 1. In this step, we combine like terms on both sides of the equation.
The property that justifies step 1 is the Associative Property of Addition. This property allows us to rearrange the terms of an addition expression without changing their sum. The equation 6x + 2x - 2 = 30 has two terms with x, namely 6x and 2x. According to the Associative Property of Addition, we can group these terms together since they have the same variable, x.
Therefore, we can rewrite the equation as (6x + 2x) - 2 = 30. By combining the like terms 6x and 2x using the Associative Property of Addition, we simplify the equation to 8x - 2 = 30 and proceed to the next step of solving the equation.