Question

Identify the property that justifies each step asked about in the answer area below. Line 1: \text{Line 1: }\phantom{=}Line 1: = 4(8+9x)\,\,4(8+9x)4(8+9x) Line 2: \text{Line 2: }\phantom{=}Line 2: = 4(9x+8)\,\,4(9x+8)4(9x+8) Line 3: \text{Line 3: }\phantom{=}Line 3: = 36x+32\,\,36x+3236x+32 Line 1 to Line 2: Line 2 to Line 3:

Answer 1

Answer:

1. Commutative Property of Addition

2. Distributive property

Step-by-step explanation:

Given

$Line 1: 4(8+9x)$

$Line 2: 4(9x+8)$

$Line 3: 36x+32$

Required

Justify each step

From Line 1 to 2:

The property from Line 1 to 2 depicts $a + b = b + a$;

i.e.

$4(8 + 9x) = 4(9x + 8)$

This is referred to as Commutative Property of Addition

From Line 2 to 3:

The property here depicts $a(b + c) = a * b + b * c$

i.e.

$4(9x + 8) = 4 * 9x + 4 * 8$

$4(9x + 8) = 36x + 32$

This is referred to as Distributive property