Question

When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step:

Original Equation: 3x + x^2 - 1 = 0
First Step: x^2 + 3x - 1 = 0
a) The Associative Property
b) The Commutative Property
c) The Distributive Property
d) The Addition Property of Equality

Answer 1

Emily used the Commutative Property to rearrange the terms when solving the equation, which allows the terms in an addition to be moved without changing the sum.

Step-by-step explanation:

When Emily rewrites the original equation 3x + x^2 - 1 = 0 to x^2 + 3x - 1 = 0, she is using the Commutative Property of addition. This property allows her to rearrange the terms in the equation because adding numbers in any order does not change the sum. The commutative property is specifically applicable to addition and multiplication and states that a + b = b + a. The properties of the commutative, associative, and distributive are fundamental to solving equations in algebra.