Question

Identify the property that justifies each step asked about in the answer area below.
Line 1: (−8+4x)+9
Line 2: (4x+(−8))+9
Line 3: 4x+(−8+9)
Line 4: 4x+1

Answer 1

To justify each step in the simplification from Line 1 to Line 4, we can identify the underlying properties used:

**Line 1**: (−8 + 4x) + 9
**Line 2**: (4x + (−8)) + 9
**Justification for Line 1 to Line 2**: Commutative Property of Addition
(This property states that the order in which numbers are added does not change the sum.)

**Line 3**: 4x + (−8 + 9)
**Justification for Line 2 to Line 3**: Associative Property of Addition
(This property states that the way in which numbers are grouped when adding them does not change the sum.)

**Line 4**: 4x + 1
**Justification for Line 3 to Line 4**: Simplification / Combining Like Terms
(This step involves calculating −8 + 9, which equals 1.)

In summary:
- Line 1 to Line 2: Commutative Property of Addition
- Line 2 to Line 3: Associative Property of Addition
- Line 3 to Line 4: Simplification / Combining Like Terms