Math Problem Statement

Using the two-column proof above, identify the missing property that justifies the second step (fills in the first blank).

Solution

The goal is to identify the property that justifies the second step of the two-column proof, which involves changing the order of terms in the given expression.

Here’s a breakdown of the first two steps:

  1. Given Expression: 8i62015i8i - 6 - 20 - 15i
  2. Rewriting Terms: 620+8i15i-6 - 20 + 8i - 15i

This step involves rearranging the terms, specifically switching the position of 620-6 - 20 and 8i15i8i - 15i.

Justification:

The property that allows us to rearrange the terms in addition is the Commutative Property of Addition. This property states that the order of terms in an addition operation can be changed without affecting the sum.

Answer:

c. Commutative Property of Addition


Let me know if you’d like further clarification or a detailed explanation of any step!

Here are 5 related questions to expand on this topic:

  1. What is the Commutative Property of Addition, and how does it differ from the Associative Property?
  2. How is the Distributive Property of Addition used in solving algebraic expressions?
  3. What role does the Inverse Property of Addition play in simplifying expressions?
  4. What is the importance of the Substitution Property in proofs?
  5. How can the Associative Property of Addition help group terms when solving equations?

Tip: In algebraic proofs, always identify whether you are rearranging, regrouping, or simplifying terms to determine the correct property.

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Math Problem Analysis

Mathematical Concepts

Algebra
Properties of Addition
Complex Numbers

Formulas

a + b = b + a (Commutative Property of Addition)

Theorems

Commutative Property of Addition

Suitable Grade Level

Grades 9-12