-7(x – 4) = -7x + 28
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1 point
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Substitution Property
Reflexive Property
Symmetric Property
Transitive Property
Distributive Property
The correct answer is Distributive Property.
To solve the equation -7(x – 4) = -7x + 28, we can apply the Distributive Property of multiplication over addition/subtraction.
The Distributive Property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
In this case, we have -7 multiplied by the expression (x – 4). Distributing -7 into the parentheses, we get:
-7(x – 4) = -7 * x + (-7) * (-4)
Simplifying further:
-7(x – 4) = -7x + 28
As you can see, the Distributive Property was used in this step.
To solve this equation, we need to simplify both sides of the equation by using different properties of equality. Let's go step by step.
The given equation is:
-7(x - 4) = -7x + 28
To simplify, we'll start by using the distributive property. The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this case, -7 is multiplied by the expression (x - 4), so we need to distribute -7 to both terms inside the parentheses:
-7 * x + (-7) * (-4) = -7x + 28
Simplifying further, we get:
-7x + 28 = -7x + 28
At this point, we notice that the equation is simplified, and both sides are equal. This means that we have an identity, and the solution to this equation is all real numbers.
So, the correct answer to the question about which property is used is the Reflexive Property, which states that a = a.
Therefore, the answer is:
Reflexive Property.