Question

Identify the property that justifies each step in the simplification of the expression:

Line 1: (-3 + 4x) + 8
Line 2: (4x + (-3 + )) + 8
Line 3: 4x + (-3 + 8)
Line 4: 4x + 5

A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property

Answer 1

The Commutative Property of addition justifies the rearrangement of terms from Line 1 to Line 2, and the Associative Property of addition justifies the regrouping of terms from Line 2 to Line 3. The final step from Line 3 to Line 4 is the simplification of terms inside the parentheses.

Step-by-step explanation:

The student is asking for the identification of the property that justifies each step in the simplification of a mathematical expression. These concepts typically pertain to algebraic manipulations common in high school mathematics curriculum.

• Line 1 to Line 2: This step shows the reordering of the terms inside the parentheses, which is justified by the Commutative Property of addition (A+B = B+A).
• Line 2 to Line 3: This step involves regrouping the terms inside the parentheses, which is justified by the Associative Property of addition ((A+B)+C = A+(B+C)).
• Line 3 to Line 4: In this step, the numbers inside the parentheses are simplified by performing the addition, which reduces to adding 5 to 4x, obtaining the final simplified form 4x + 5, using the property of addition for negative and positive numbers.