Questions: Choose the property of real numbers that justifies the equation. m+2=2+m (Choose one) d * 0=0 -b+b=0 (Choose one) 7 (8 n)=(7-8) * n (Choose one)

Transcript text: Choose the property of real numbers that justifies the equation. $m+2=2+m$ (Choose one) $d \cdot 0=0$ $-b+b=0$ (Choose one) $7 \cdot(8 \cdot n)=(7-8) \cdot n$ (Choose one)

Solution

Solution Steps

To solve this problem, we need to identify the properties of real numbers that justify each given equation. The properties include the commutative property, associative property, identity property, and distributive property, among others. We will match each equation with the appropriate property.

Step 1: Identify the Properties of Real Numbers

We need to match each equation with the appropriate property of real numbers. The properties include:

Commutative Property: $ a + b = b + a $ or $ a \cdot b = b \cdot a $
Associative Property: $ (a + b) + c = a + (b + c) $ or $ (a \cdot b) \cdot c = a \cdot (b \cdot c) $
Identity Property: $ a + 0 = a $ or $ a \cdot 1 = a $
Distributive Property: $ a \cdot (b + c) = a \cdot b + a \cdot c $
Zero Product Property: $ a \cdot 0 = 0 $
Inverse Property: $ a + (-a) = 0 $

Step 2: Match Equations with Properties

We analyze the given equations:

$ m + 2 = 2 + m $ is justified by the Commutative Property.
$ d \cdot 0 = 0 $ is justified by the Zero Product Property.
$ -b + b = 0 $ is justified by the Inverse Property.
$ 7 \cdot (8 \cdot n) = (7 \cdot 8) \cdot n $ is justified by the Associative Property.