Identify the property that justifies step 3 when solving the given equation, given equation is 6x+2(x-1)=30 and step 3 is 8x-2+2=30+2
The property used in step 3 when solving the equation 6x + 2(x-1) = 30 is the distributive property.
This property states that for any real numbers a, b, and c, a * (b + c) = a*b + a*c.
In step 3, the distributive property is applied to the expression 2(x-1). The 2 is multiplied by both the x and the -1, resulting in 2*x - 2. So, 2(x-1) = 2*x - 2.
Using this property, the equation can be rewritten as 6x + 2x - 2 = 30. Then, in step 3, the equation becomes 8x - 2 + 2 = 30 + 2.
The property that justifies step 3 when solving the given equation 6x + 2(x-1) = 30 is the Distributive Property.
Step 3: 8x - 2 + 2 = 30 + 2
In step 3, the Distributive Property is used to distribute the coefficient "2" to both terms inside the parentheses. By applying the Distributive Property, the equation is expanded to 8x - 2 + 2, which simplifies to 8x. Similarly, 30 + 2 simplifies to 32.
Step 3 in the given equation involves simplifying both sides of the equation by applying the distributive property. The distributive property allows us to distribute or multiply a number to each term inside parentheses.
In this case, we have 6x + 2(x - 1) = 30. To simplify the left side of the equation, we distribute the 2 to both terms inside the parentheses:
6x + 2 * x - 2 * 1 = 30.
This results in:
6x + 2x - 2 = 30.
To further simplify, we combine like terms on the left side of the equation:
(6x + 2x) - 2 = 30.
This gives us:
8x - 2 = 30.
The distributive property justifies this step. It allows us to distribute the number outside the parentheses to each term inside, which simplifies the equation by eliminating the parentheses.