Question

the expression (6 + 9x) + 4x is simplified in several steps below. for each step, choose the reason that best justifies it. step reason (6 + 9x) + 4x given expression 6 + (9x + 4x) select 6 + 13x select 13x + 6 select

Explanation:

Step 1: Justify \( 6+(9x + 4x) \)

The associative property of addition states that for any real numbers \( a \), \( b \), and \( c \), \( (a + b)+c=a+(b + c) \). Here, \( a = 6 \), \( b = 9x \), and \( c = 4x \), so we applied the associative property of addition to group \( 9x \) and \( 4x \) together.

Step 2: Justify \( 6 + 13x \)

To simplify \( 9x+4x \), we use the distributive property (or the concept of combining like terms). The distributive property states that \( ax+bx=(a + b)x \). Here, \( a = 9 \), \( b = 4 \), so \( 9x+4x=(9 + 4)x=13x \), which is combining like terms.

Step 3: Justify \( 13x+6 \)

The commutative property of addition states that for any real numbers \( a \) and \( b \), \( a + b=b + a \). Here, \( a = 6 \) and \( b = 13x \), so we applied the commutative property of addition to rearrange the terms.

Answer:

s for each step:

• For \( 6+(9x + 4x) \): Associative Property of Addition
• For \( 6 + 13x \): Combining Like Terms (using the Distributive Property)
• For \( 13x+6 \): Commutative Property of Addition