Question

When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
Original Equation:
Original Equation:
4, plus, left parenthesis, 3, plus, x, right parenthesis, equals, 4
4+(3+x)=
4
First Step:
First Step:
left parenthesis, 4, plus, 3, right parenthesis, plus, x, equals, 4
(4+3)+x=
4
Answer
Multiple Choice Answers
division property of equality
distributive property of multiplication over addition
associative property of addition
multiplication property of equality

Answer 1

Carmen's first step in rearranging the equation \( 4 + (3 + x) = 4 \) to \( (4 + 3) + x = 4 \) involves regrouping the terms in the expression on the left side of the equation.

This rearrangement is justified by the **associative property of addition**, which states that the way in which numbers are grouped in addition does not change their sum.

So the correct answer is:

**associative property of addition**.